SSLC Mathematics Part 1 (English) YK Notes

1. Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the
ratio 2 : 3.

Let the Coordinates of the Points be(x,y)

( ) (− ) ( ) ( − )
( ) ( ) -1 7 4 -3
( ) ( ) ( ) ( )
= ( )
= ( )
= ( )
⇒( )= ( )
2. Find the coordinates of the poin ts of trisection of the line segment join ing (4, –1) and
(–2, –3).
Let P and Q are the trisection points of AB
-1 7 4 -3
⇒ AP = PQ = QB
∴ The point P divides AB internally in the ratio 1 : 2
( ) ( − ) ( ) (− − )
∴ The coordinates of P is,
( ) ( )
( ) ( ) ( ) ( )
= ( )
= ( )= ( )
= ( )
The point Q divides AB internally in the ratio 2 : 1
( ) ( − ) ( ) (− − ) ;
( ) ( ) [Using section formula]
( ) ( ) ( ) ( )
= ( )
= ( )
= ( )
= ( )
3. To conduct Sports day activities in your rectangular shaped school groun ABCD, lines have
been drawn with chalk powder at a distance of 1m each. 100 flower pots have been placed at a
distance of 1m from each other along AD, as shown in fig 7.12. Niharika runs th the distance AD
on the 2nd line and posts a green flag. Preet runs th the distance AD on the eight line and posts a
red flag. What is the distance between both the flags? If Rashmi has post a blue flag exactly
halfway between the line segment joining the two flags, where should she post her flag?

Solution: The distance of green flagposted by Niharika on the 2nd line

5
The distance of red flag posted by Preet on the 8th line

Coordinates of Green flag ( 5) ( )

Coordinates of red flag ( ) ( )
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SSLC Mathematics Part 1 (English) YK Notes
The distance between flags
d √( − ) +( − )

d √( − ) +( − 5)
√( ) +(−5)
√ + 5
√
The coordinates of blue flag, if Rashmi post in between these two flags be
( ) ( )
( )
( )
(5 5)
4. Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (– 1, 6).
( ) (− ) ( ) (− ) ( ) ( − )
( ) ( )
) ( ) ( ) ( )
(− ) ( ) -3 10 6 -8
− Or
− − −
⇒ − − − +
⇒ − −

We should verify that the ratio satisfies the y-coordinate also

( ) ( )

∴ the point (– 1, 6) divides the line segment joining the points A(– 3, 10) and
B(6, – 8) in the ratio 2 : 7
5. Find the ratio in which the line segment joining A(1, – 5) and B(– 4, 5) is divided by thex-axis. Also
find the coordinates of the point of division.
− ( ) Let the ratio be
( ) ( −5) ( ) (− 5)
( ) ( )
( ) ( ) ( ) ( )
( ) ( )

⇒ 5 −5
⇒5 5
⇒ , the ratio is
( ) ( )

−
∴ The coordinates of the point of division = ( )
6. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Solution:Let A(1,2), B(4,y), C(x,6) and D(3,5) are the vertices of the parallelogram.
Since ABCD is a parallelogram
Therefore diagonals AC and BD bisects each other.
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SSLC Mathematics Part 1 (English) YK Notes
So, the coordinates of both AC and BD are same.
∴ Mid point of AC = Mid point of BD ( )
( ) ( )
⇒ ( ) ( )
⇒
⇒ + d 5+
⇒ − d −5
⇒
7. Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, – 3)
and B is (1, 4).
The center of the Circle is the mid-point of the diameter
∴( ) ( − ) ( ) ( ) ( )
( ) ( )
( − ) ( )
⇒ −
⇒ + + −
⇒ − − −
⇒ −
∴ The coordinates of a point A is ( − )
8. If A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP = AB
and P lies on the line segment AB
Given AP = AB
divides AB in the ratio 3:4
⇒ -2 -2 2 -4
( ) ( )
( ) ( ) ( ) ( )
= ( )
= ( ) = ( )
9. Find the coordinates of the points which divide the line segment joining A(– 2, 2) and B(2, 8)
into four equal parts
The point divides AB in the ratio
The coordinates of is,
( ) ( ) -2 2 2 8
( ) ( ) ( ) ( )
= ( )
= ( )
= ( )
(− )
The point is the mid-point of AB. The coordinates of
( ) ( )
= ( )

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SSLC Mathematics Part 1 (English) YK Notes
= ( ) = ( 5)
The point divides AB in the ratio , The coordinates of is,

( ) ( )
( ) ( ) ( ) ( )
= ( )
= ( )
= ( )
( )
10. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken in
order[Hint: Area of rhombus = (product of its diagonals)]
√(− − ) +( − ) √(− ) +( )
√ + √ √
√(− − ) +(− − 5) √(− ) +(− )
√ + √ √
The area of the rhombus √ √
(√ )
( ) square units.
7.5 Summary

1. The distance between two given points d √( − ) +( − )

2. The distance from the orgin to the given points d √ +
3. Section formula :P is the point which divides the line segment joining the points ( ) and
( )
If the point divides the line in the ratio then the coordinates of P

( ) ( )

4. If P is the midpoint of AB, it divides in the ratio 1:1

( ) ( )

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