If Q 0 , 1 is equidistant from P 5 , - 3 and R x , 6 , find the values of x . Also find the distances Q R and P R .

According to the question, given Q 0 , 1 is equidistant from P 5 , - 3 and R x , 6 So, P Q = Q R Using distance formula: ⇒ x 1 - x 2 2 + y 1 - y 2 2 ⇒ 5 - 0 2 + - 3 - 1 2 = 0 - x 2 + 1 - 6 2 ⇒ 5 2 + - 4 2 = - x 2 + - 5 2 ⇒ 25 + 16 = x 2 + 25 Squaring on both sides, 25 + 16 = x 2 + 25 ⇒ 16 = x 2 ⇒ x = ± 4 Hence, point R is 4 , 6 or - 4 , 6 Case (i): When point R is 4 , 6 P R = 5 - 4 2 + - 3 - 6 2 = 1 2 + - 9 2 = 1 + 81 = 82 Q R = 0 - 4 2 + 1 - 6 2 = - 4 2 + - 5 2 = 16 + 25 = 41 Case (ii): When point R is - 4 , 6 P R = 5 - - 4 2 + - 3 - 6 2 = 9 2 + - 9 2 = 81 + 81 = 9 2 Q R = 0 - - 4 2 + 1 - 6 2 = 4 2 + - 5 2 = 16 + 25 = 41 Hence, x = ± 4 , Q R = 41 , P R = 82 , 9 2

To conduct Sports Day activities, in your rectangular shaped school ground A B C D , lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along A D , as shown in Fig. Niharika runs 1 4 t h the distance A D on the 2 n d line and posts a green flag. Preet runs 1 5 t h the distance A D on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

According to the question, it is given that Niharika posted the green flag (G) at 1 4 t h the distance A D i . e . 1 4 × 100 = 25 m from the starting point of 2 n d line. So, coordinates of this point G are ( 2 , 25 ) . Similarly, Preet posted red flag at 1 5 th the distance A D i . e . 1 5 × 100 = 20 m from the starting point of 8 t h line. So, coordinate of this point R is 8 , 20 . Now, below is the figure, which simplifies the given question by considering G as a position of green flag posted by Niharika and similarly R as a position of red flag posted by Preet. Now distance between these flags by using distance formula = G R G R = 8 - 2 2 + 20 - 25 2 = 36 + 25 = 61 m Since it is given that Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags . Now the point at which Rashmi should post her blue flag is the midpoint of line joining these points. Let this point be B x , y . x = 2 + 8 2 , y = 25 + 20 2 x = 10 2 = 5 , y = 45 2 = 22 .5 So, B x , y = 5 , 22.5 So, Rashmi should post her blue flag on 5 t h line at a distance of 22.5 m .

E M B I B E

MATHEMATICS Textbook for Class X>Chapter 7 - Coordinate Geometry>Exercise 7.1>Q 7

HARD

10th Assam Board

IMPORTANT

Earn 100

Find the point on the $x -$ axis which is equidistant from $(2, - 5)$ and $(- 2, 9)$ .

Important Questions on Coordinate Geometry

HARD

10th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 7 - Coordinate Geometry>Exercise 7.1>Q 8

Find the values of

y

for which the distance between the points

P (2, - 3)

and

Q (10, y)

is

10

units.

HARD

10th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 7 - Coordinate Geometry>Exercise 7.1>Q 9

If

Q (0, 1)

is equidistant from

\Rightarrow 8 k = - 56

and

R (x, 6)

, find the values of

x

. Also find the distances

Q R

and

P R

.

EASY

10th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 7 - Coordinate Geometry>Exercise 7.1>Q 10

Find a relation between

x

and

y

such that the point

(x, y)

is equidistant from the point

(3, 6)

and

(- 3, 4)

.

MEDIUM

10th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 7 - Coordinate Geometry>Exercise 7.2>Q 1

Find the coordinates of the point which divides the join of

(- 1, 7)

and

(4, - 3)

in the ratio

2 : 3

.

HARD

10th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 7 - Coordinate Geometry>Exercise 7.2>Q 2

Find the coordinates of the points of trisection of the line segment joining

(4, - 1)

and

(- 2, - 3)

.

HARD

10th Assam Board

IMPORTANT

MATHEMATICS Textbook for Class X>Chapter 7 - Coordinate Geometry>Exercise 7.2>Q 3

To conduct Sports Day activities, in your rectangular shaped school ground $A B C D$ , lines have been drawn with chalk powder at a distance of $1 m$ each. $100$ flower pots have been placed at a distance of $1 m$ from each other along $A D$ , as shown in Fig. Niharika runs $\frac{1}{4} t h$ the distance $A D$ on the $2^{n d}$ line and posts a green flag. Preet runs $\frac{1}{5} t h$ the distance $A D$ on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?