ST.

MICHAEL’S ACADEMY
STD: X MATHEMATICS MARKS : 50
23.07.2025 CHAPTER TEST TIME: 1 hr 45 min.
(Section formula)

SECTION – A
Answer all the questions (10)
01. (i) The point which divides the line segment joining the points A(7, -6) and
B(3, 4) in the ratio 1 : 2 internally lies in the ______ quadrant.
a) I b) II c) III d) IV
(ii) Assertion (A) : The line segment joining the points (-5,8) and (10, -4) is
trisected by the co-ordinate axes.
Reason (R) : In any right triangle, the midpoint of hypotenuse is
equidistant from the three vertices.
a) Both A and R are true and R is the correct explanation of A.
b) Both A and R are true and R is not the correct explanation of A.
c) A is true R false d) A is false R is true
(iii) If x-2y+k = 0 is a median of a triangle ABC from A to BC whose
vertices are (-2,3), (0,4) and (2,2). Then the :
I. value of k is 8.
9
II. co-ordinates of centroid of ∆ABC is (0, ).
2
III. co-ordinates of the midpoint of the line AB is (-1,6).
Which of the following statement is/are correct?
a) Only I b) Only II c) Only III d) Only I and II
(iv) Assertion (A) : If the points A(x,1),B(8,2),C(9,4) and D(7,3) are the
vertices of a parallelogram taken in order, then the value
of x is 5.
Reason (R) : Diagonals of a parallelogram bisect each other at right
angles.
a) A is true, R is false b) A is false, R is true
c) Both A and R are true d) Both A and R are false
(v) While on a road trip with his friends, the wheel of Amar’s vehicle got
stuck in ice. With no help in sight, he managed to use a makeshift lever
to raise the wheel and were
safe.
If the point P(2, 1) lies on the
line segment joining the two
points A(4,2) and B(8,4) lying
on the wheel then :
1
a) AP = AB b) AP =AB
3
1 1
c) PB = AB d) AP = AB
3 2
 (vi) The Dockland building at the port of Hamburg is an astounding perfect
parallelogram and an architectural marvel. If A(2,1), B(3,4),C(5,5) are
the three vertices
of the figure. Then
the fourth vertex is
a) (1, -2)
b) (2, 1)
c) (-1, 2)
d) (1,2)

(vii) Assertion (A) : The co-ordinates of one end of a diameter of a circle is

(1, 4). If its centre is at (2, -3), then the co-ordinates of
the other end of the diameter is (-3, -10)
Reason (R) : Centre of a circle is equidistant from each end of a
diameter.
a) Both A and R are true and R is the correct explanation of A.
b) Both A and R are true and R is not the correct explanation of A.
c) A is true R false d) A is false R is true
(viii) If the points P(6,-3) lies on the line segment joining points A(4, 2) and
B(8,4) , then
1 1 1 1
a) AP = AB b) AP = AB c) BP = AB d) AP = AB
3 4 3 2
ix) The line segment joining the points A(5,-2) and B(9,6) is divided in the
ratio BP : AP = 1 : 3, the point P is
7
a) (4, -7) b) ( , 4) c) (8, 4) d) (12, 8)
2
x) If the point P(k,0) divides the line segment joining the points A(2, -2)
and B(-7,4) in the ratio 1 : 2, then the value of k is
a) -2 b) -1 c) 1 d) 2

SECTION – B
2. a) A line segment directed from (-3, 2) to (1, -4) is trebled. Find the co-ordinates
of the terminal point. (3)
b) The line segment joining the points (2, -2) and (4, 6) is extended each way a
distance equal to half of its own length. Find the co-ordinates of its terminal
points. (3)
c) Show that the line segment joining the points A(-5, 8) and B(10, -4) is trisected
by the co-ordinate axes. Also find the points of trisection. (4)
3. a) A line segment from A(-1,4) to B(2, 3) is produced to C so that AC = 3AB.
Find the co-ordinates of C. (3)
 b) In the ΔABC, AD is the median. If A(5, -3) and D(1,9). Find the co-ordinates
of the Δ. (3)
c) D, E, F are respective midpoints of three sides BC, CA and AB of the ΔABC.
7 5 1 −1
If D(1, ), E( , ) and F( , −1) then find the centroid of the Δ. (4)
2 2 2 2
4. a) Calculate the ratio in which the line segment joining A(6, 5) and B(4, -3) is
divided by the line y = 2 (3)
b) Find the co-ordinates of the points which divide the line segment joining the
points A(4, -8) and B(8, 0) into four parts. (3)
c) The line joining P(-4, 5) and Q(3, 2) intersects the y axis at R. PM and QN are
perpendicular from P and Q on the x axis. Find
(i) the ratio PR : QR
(ii) co-ordinates of R
(iii) Area of quadrilateral PMNQ (4)
5. a) Find the ratio in which the line segment joining the points A(7, -1) and B(2, 4)
is divided by the line 2x + y -9 =0. Find the point of intersection. (3)
b) G(1, 2) is the centroid of the ΔABC, if B is (4, 1).Find the midpoint of AC. (3)
c) In the given figure, if the line segment AB is intercepted by the y axis and x
axis at C and D respectively., such that AC : AD = 1:4 and D is the midpoint
of CB. Find the co-ordinates of D,C and B. (4)