x Practice Exercise Q14. The distance of the points (0, 3) and (0, — 5) Multiple choice Questions y from Y-axis 1s: Q1. The point which fies on Y-axis ata distance of 4 45 ve dist Ba en8 ao 4 units in the negative direction of Y-axis is: - " 2. 0,4) b. (4,0) BC Saat © .-4) 4,0) al bs 10 d.i2 Q2. Which point lies on X-axis? Q16. Theimage of point (-3,4) with respect to X-axis 2.2) b.(3,2) ©. 2.0) 1,2) 3. Which point lies on Y-axis? 2.1.3) b.(0, 3) <.6.2) d G23) Q4. Which point lies to theFight Of Yeaxist 2. (0,3) <@§) ce between the points A(3, 5) and 6.8.4) 4.3.4) of a point P(— 8, 5) with respect to Qu, b.@5) d. (0,5) O16) Which of the points P(“1,1), Q (3,4), RU-1), S(-2,-3)and T(4, 4) lie inthe IV quadrants? Q5. ‘The perpendiciilar distance of the point P(2, 5) a. Rand T 6. QandR fromthe ¥: c onlys dP ande Q19. In the following \graph the coordinates of A - ) as b.2 re) 44 Q6. Which point lieson thefeft of Y-axis? 2.20) 6. (2,4) < 5,2) 4.3, 6) Q7. Which point lies above X-axis? a (-L2) _b.(2.0) | ab PPC, -a) } QB. IF the coordinates of two points are P(-2, 3) and Q(-3, 5), then (abscissa of ?) ) — (abscissa of Q) is: as \bi jangle de ) ao. theortinde ota point iS negative in: | a. tl and ll quedrent® b. ll quadrantonly c. land IV quadrants: 4. IV quadrant only c ‘ } Q10. Which point lies in IV.quadrantt @ Assertion & Reason type Questions y 3. (3,4) be) Directions (Q. NOs. 20-23): In the following questions, a 2,3) .(0, 1) statement of Assertio# (A) is followed by a statement of a QUL If(x +3, 5) =(6, y—3), then coordinates(x,,y)_ Reason (R)ChOose the correct option: a. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of a. (2,3) b. 2-8) © 23) a-2-3) are: a. (3,2) b.3,8) Assertion (A) Esa dG, 8) ®. Both Assertion (A) and Reason (R) are true but Q12. Ifthe points P(0,—2), Q(0,4) and Rla—5, 6) arelie Reason (R) is not the correct explanation of on Y-axis, then the value of ais: Assertion (A) a-5 bs cé d.4 c Assertion (A) is true but Reason (R) is false. 18. The coordinates of any point on the Y-axis are d. Assertion (A) is false but Reason (R) is true. of the form (0, k), where |k| is distance of the Q20. Assertion (A): The point (-3, 0) lies on Y-axis point from the: and (0, 4) lies on X-axis. a Neatly baveaits Reason (R): Every point on the X-axis has zero distance from X-axis and every point on the Y-axis has zero distance from Y-axis. c. (0,1) (0, 5) ee2 27, , 20. (d) Assertion (A): Point (~: 22, 23, 24. 25, 26. 28. 29, 31. 32. In the given points, only points Q(3, ~ 4) and R(L.-1) has x-coordinate positive and y-coordinate negative. So, it ies in IV quadrant. (b) The coordinates of A are (2, -3). , 0) has y-coordinate zer0, so it lies on X-axis. And point (0, 4) has xccoordinate zero so it lies on Y-axis. Thus, Assertion (A) is false. Reason (R): It is true to say that every point on the X-axis has zero distance from X-axis and every point on the Y-axis has zero distance from Yeaxis. Hence, Assertion (A) is false but Reason (R) is true. (a) Assertion (A): tis true to say that the ordinate of a point (3, 7) is 7, whieh is perpendicdlar distance from point to the X-ais, Reason (R): It is /alsof title to"Say thatthe perpendicular distance ofta.point from X-axis is said to be an ofdinate. Hence, both/Asgertioff (A) and Reason (R) are true and Reason (R).'5 the/correct explanation of Assertion (A), (b) Assertion (A): Itis true to say that point @, = 4) ligs in IV quadrant. Reason (R): Itis also true to say that point having sign of the form (-, +) lies in the I! quadrant, Hence, both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion\(A), (d) Assertion (A): If the ordinate of a point is equal to its\absciss8, then point lies either in the Ist quadrant or imaié lind quadrant. So, Assertion (A) is false Reason (R): It is\truélto say that 2'paint having both coordinates ate negative, it will be tirtird quadrant. Hence, Assertion (A) is false but Reason|(R) is tue. negative origin The distance of the point (~ 4, ~ 2) from Y-axis is positive value of x-coordinate Le, 4 In Yeaxis, x-coordinate is zero. Therefore the coordinate of required point is (0, 3. 0.0) True False False Point (-2, -1) has both coordinates are negative so it lies in ill quadrant. Hence, given statement is false. 30. False Hy Case Study Based Questions y Case Study 1 QL Q2. Q3. a4. Qs. A new year party is organised by Anil on 31st December. Anil invites some of his friends to have some fun and wants to enjoy the delicious food. Among all of the friends, four friends Reena, Vishal, Anshul and Ashwani are standing at positions A(3, 5), B(~ 3, 5), C(~ 3, ~ 5) and D(3,—5) respectively. On the basis of the dbove tnfohmation, solve the following question; ‘The position of given points aré shown below. ‘The perimeter of this figure is: ¥ ® A isha Bien) Gs a5) x Pe Ex =a 1 pat jp a A 3 “4 Anshul) shoeon D as y a5 030 b32 6.16 d.20 Anshul stands on the quadrant: al bl cll aw ‘The distance between Reena and Vish: 2.10 bo <6 a8 Area of rectangle ABCD is: a. $0 sq. units b. 60 sq. units 65 5q. units 4.55 sq, units The distance of Reena from origin is: a. ¥34 units b. ¥30 units c ¥39 units d. ¥29 units eeQ2. The area of given figure is: Case Study 4 ; SB aank : 435 ats Four friends Aakunsha, Prabhat, Puneet and Q3. The coordinates of intersection point of eS diagonaisare respectively. This park has been divided into small 264 b (46) ce46) 422) squares by drawing equally distanced horizontal Q4. The perimeter of a square is: and vertical lines. Consider XOX’ and YOY" as a. 14 units b. 12 units coordinate axes. ¢. 16 units d. 18 units QS. ‘The image of a point D(2, 8) with respect to X-axis is: _ a. (-2,-8) b.-28) (8,2) d. (2, 8) = . Solutions = 1. (b) From figure, AB = CD = 4 and AD = BC 24 AC = YiAB)? + BQ? = fy A= 42 Similarly, ep 4? Since, all sides and diagonals,of a figure are equal. So, ABCD forms alquare. > So, option(b)isveorrect. i 2. (¢) The aga of given figure = Area of square On the basis of the above information, solve the following questions 16 squnits QL So, option Tefislesrrgct. Q2. Inwhich quadrant, point A is located? 3. (b) The intersection point of two diagonals is E. Q3. Find the image of a point A with respect to a 0@.8) (6, 8) UR Q4. Find the area of figure. © Solutions * 1. The perpendicular distafice Of B from y is 2 in positive direction atid perpendicular distance of 8 from ¥-anis is3 inynegative direction of Y-axis. Hence, coordinates off are (2, — 3). Poifif\A is located islll quadrant. 3. The cOortlinate6f point Ais (~3, - 3). The image ofa point aC 3, 3) with respect to Y-axis (3, - 3) 4._Now?length of AB = |- 3] +2 234255 Height = perpendicular distance of D from AB =4 Area of parallelogram = length x height x 4= 20 sq. units The coordinates of E are (4, 6) So, option (b) is correct. (c) The perimeter of a square Case Study 5 Annie Besant school provides good and quality (sicle) 4x4 =16 units, So, option (c) is correct. (d) The image of a point O(2, 8) with respect to Xaxis is (2-8), So, option (d) is correct education. The school also provides playing facilities to students for which they created wo playground one is in the shape of rectangle and the other one is triangular in shape, which is as shown below | | | | | | | | | | | | | | | | | Find the coordinates of B. | | | | | | | | | | | | | | | | |, Q3. In figure, LM isa line parallel to the Y-axis at a distance of 2 units. (i) What are the coordinates of thepints P and Q? (ii) What is the difference betWeen thé absciss3\of the points L and Mz ¥ Q4. Which of the following points lie on (i) X-axis, (ii) Y-axis? A (0, 2), BGS, 6)C(23, 0).D(0, 23), E (0, 4), F(6, 0), GG, 0), Find the area of KAOB. Given mirror image of A’ and B’ on X-axis are respectively Ajand B. ¥ Qs. 4-498 “a wi) t Q6. In the following figure, write the coordinates of its vertices. Also, find the area of figure. Q7._(i) Name the figure MNOP. (ji) Filid-the perimeter of figure. y eie.3) Mia, 3) TT Nia.) tT2g4 Q8. Write coordinates of point of intersection of 09.3) ). Short Answer Tijpe-ti Questions W QL Write the coordinates of the point: (whith lies on X and Y-axes both. (ii) whose abscissa is 5 and ordinate is 6. (iii) whose ordinate is 6 and which lies on Y-axis. (iv) whose ordinate is 3 and abscissa is ~7. (v) whose abscissa is 3 and which lies on X-axis. (vi) whose abscissa is 4 and ordinate is 4. Q2. Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units, respectively such that one vertex at the origin, the longer side lies on the X-axis and one of the vertices lies in III quadrant. Also, find the length of diagonal AC. | | | | | | | | | | | | | | | | | diagonals, Also.find the area of figure. | | | | | | | | | | | | | | | | fs eeVery Short Answer Type Questions 1. The ordinates ie, y-coordinate of the given points are 4, 0, -5 and -2. 2. This point will ie on the X-axis. 3. Perpendicular distance of the point from Y-axis, = coordinate of point (5,7) = 5. 4. (i) Point (-6, 2) has x-coordinate is negative and y-coordinate is positive so it lies in Il quadrant. (i Point 5, -4) has both coordinates are negative, so it lies in Ill quadrant. Distances of point C(-3, -2) from X-axis is 2 units in the negative direction and from, Yoanis is 3 units in the negative directioneDistances of point D(5, 2) from X-axis is 2uhits iqthe positive direction and from Y-axis 5.untts injthe positive direction. 6. (Abscissa of A) — (Abscifsa off8) = -3 (6723 7. Given, (a, b) = (0/-2) Compare x and y-cdordinates Both sides, af Oand.b = -2 8. Since, P(ab) liesvifiithe IV quadrant. o> Oantb Jo Hence, a> 9. Since paint (3, a -3) lies on X-axis ie, ordinate of point C= 5-320) =3 Hence, the value of ais 3 10. Such a point will ie in tl and IV quadrants. LL. TiP in reflection of PyrbudlPregpebafa Yani, the sgh of x-coordinate will be changed. The reflection of 3, -2) in Y-axis is (8)—2). 12. Given, y-5©0 =\yeS Hence, one solution canbe (0,5) 6r (1,5) of(2)5) Short Answer Type-1 Questions 1. @ Since the point lies on X-axis at a distance of 9 units in positive direction from Y-axis, hence, its coordinates are (9, 0) (i Since the point lies on Y-axis at distance of 9 units in negative direction from X-axis, hence, its coordinates are (0,-9). 2. Point A lies on positive X-axis at a distance of 5 units from origin = Coordinates of A are (5, 0) Point Bis ata perpendicular distance ofS units from ¥-a¥is-and 3 units from X-axis in | quadrant. JCoordinates of B are (5, 3). Point Cis Bt a perpendicular distance of 2 units from ¥-axis’and 4 unis from. X-axis in l quadrant. Coordinatesiof Gare 2, 4). Point Dies onfnegative\y-axis at a distance of Bunits fromorigit . Coordinates of Dare (0, -3), 3. (i) Point P is at alperpendiculan distance of 2 units from X-axis and, Y-axis both in | quadrant. Point Qiis at a perpendicular distance of 2 units from Y-axis and 1 unit from X-axis in IV quadrant. Coordinates of Q are (2, -1). (i) Coordinates of Ware,(2, 3) and that of M are (2, -3). Abscissa of L ‘Abscissa of M)= 2 {Required difference = 2-2= 4.) Points withy-coordinate 0 lie on X-axis. or 50 on, B. y Points C, F and G will ie on X-axis afew. (@ Points with x-coordinate 0 lie on Y-axis. 4 Points A, D and E will le on Y-axis, 5. TRICK: x x Ata 0, The micror image of (0, b) on X-axis Is (0,-b). The figure formed AOB is a right-angled triangle. Mirror image of A’ on X-axis is A(4, 4) and mirror image of B’ on X-axis is B(-4, 4), Area of AAOB =4xabx0c = hxexae 16 sq. units. | | | | | | | | | | | | | | | | | “Coordinates of P are (2, 2). | | | | | | | | | | | | | | | | | fs eeEEE EEE EEE EEE EEE EEE EEE EEE EE EEE EEE EEE EEE EEE EE EE ] Leng Answer Type Questions 2. The coordinates of vertices of given figure are a P (a, 0), Q (0, a), R (—a, 0) and S (0, —a). 1. (@ Since, given figure is a rectangle. In right-angled & ROQ, So, from the figure, the coordinates of the RQ?= OR? +09" iz ) fourth vertex are D (~1, 3) { res => RQ= OV? units | (i Length of diagonal BD = «f(a8)? + (AD) | Similarly, QP = PS = RS = av2 units ] [By using Pythagoras theorem] Also, PR = QS = 2a units ={(4P +2" So, the formed quadrilateral PQRS is a square. | Area of = (Side)? = (leva = J rea oF RUE } = 2N5 sq. units ape } ) = 2c” sq, units } TRICK: 3.” Abscissa of D = Abscissa of A= ~1 Area of rectangle - Length x Bread Otinate BD = Ordinate of C =~ 3 | a a Hence, fourth eagrdinate D is 1, ~ 3) 36 x22 a2 sqehits Hereside of arsquare is 4 units | (w Penmateropt/ raat Me Area 6f squaré ABCD = (4)? = 16 sq. units | iv) Perimeter of? (paige) and Perimeter of quate ABCD ] 2 (AB = BC) 34x Side { 6+) =Ax4 ) 816 units = 16 units | nen Chapter Test | 7 Multiple Choice Questions Q6. The distance of the point (—3, 8) from X-axis is | QL. Which point lies to the right side of Y-axis? ) 205) 63,5) c(47) d.(-4-4) TMue/False | ) Q2. Which point lies in IT quadrant? Q7. Ordinate of all the points on the Y-axis is any | 285) b63-Sc4=5) J -3,5) number. } Assertion and\Reason Type Questions DG. The distance Of ePeing (7/0) from X-axis is | ) ns (Q. Nos, 3-4) Jn the Yollowing questions, a 7 units. | )—_sttement of asset (A) & Bliare\ by stolement of Case Study Based Question Reason (R). Choose the éorrectioption. a. Both Assertion. (A) and Reason (R)-are true & 9 ‘The diagram’ sHoWs the’position of three electric and Reason (R) Ts.the corfeet explanation of poles P, Q and R were installed in a school park. } Assertion (A). Instead _of theny"Some parts of the park was not | bb. Both Assertion (A) and Rgson (Rife tygegbut lightning.S6, the management of the school ) Reason (R) is not the corréttsexplanation’of dset(€ to install one more pols inks in | Assertion (A) leeid6d to install one more pole at point $ in ) c. Assertion (A) is true but Reason (R) is false such a way that it forms. rectangle and lightened | d. Assertion (A) is false but Reason (R) is true. the maximum area of the park Q3. Assertion (A): The abscissa of a point (~2,5) is— 2. | | Reason (R): The perpendicular distance of a | point from Y-axis is said to be an abscissa. ) Q4. Assertion (A): A point whose abscissa is 4 and { ordinate is— 7 lies in IV quadrant. Reason (R): A point whose sign is the form of | ) ( +) lies in TM quadrant. in the Blanks Q5. If the abscissa is zero and the ordinate Is ) negative, then that point lies ON... + {