Question

8. Let A (-6,-5) and B (-6, 4) be two points such that a point P on the line AB satisfies
AP = 9
2 AB. Find the point P.

Answer 1

QUESTION:
Let A (-6 , -5) and B(-6 , 4) be the two points such that a point P on the line AB satisfies AP = (2/9) AB. Find the point P.

SOLUTION:
GIVEN : A (-6 , -5) and B(-6 , 4)
AP = (2/9) AB
9 AP = 2 (AP+PB)
[ AB = AP + PB]

9 AP = 2 AP + 2 PB
9 AP – 2 AP = 2 PB
7 AP = 2 PB
AP/AB = 2/7
AP: PB = 2: 7

So P divides the line segment AB in the ratio 2:7

By using Section formula internally = (m1x₂+m2x₁)/(m1+m2),(m1y₂+m2y₁)/(m1+m2)

Here, m1 = 2 & m2 = 7 , x1=-6, y1=-5, x2=-6 ,y2= 4

Coordinates of P = [(2x(-6)) + (7x(-6)] /(2+7) , [(2x(4)) + (7x(-5)] /(2+7)

Coordinates of P = (-12- 42)/9 , (8 - 35)/9
Coordinates of P = -54/9 , -21/7
Coordinates of P = (-6 , -3)

Hence, the Coordinates of P (-6,-3)

HOPE THIS WILL HELP YOU...

Answer 2

GIVEN : A (-6 , -5) and B(-6 , 4)

AP = (2/9) AB

9 AP = 2 (AP+PB)

[ AB = AP + PB]

9 AP = 2 AP + 2 PB

9 AP – 2 AP = 2 PB

7 AP = 2 PB

AP/AB = 2/7

AP: PB = 2: 7

So P divides the line segment AB in the ratio 2:7

BY SECTION FORMULA

= (m1x₂+m2x₁)/(m1+m2),(m1y₂+m2y₁)/(m1+m2)

Here, m1 = 2 & m2 = 7 , x1=-6, y1=-5, x2=-6 ,y2= 4

Coordinates of P = [(2x(-6)) + (7x(-6)] /(2+7) , [(2x(4)) + (7x(-5)] /(2+7)

Coordinates of P = (-12- 42)/9 , (8 - 35)/9

Coordinates of P = -54/9 , -21/7

Coordinates of P = (-6 , -3)