Q8 of 112 Page 146

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



⇒ 9 AP = 2 AB


⇒ 9 AP = 2(AP + PB)


⇒ 9AP = 2AP + 2PB


⇒ 9AP – 2AP = 2PB


⇒ 7AP = 2 PB


⇒


AP: PB = 7:2


So, P divides the line segment in the ratio is 2:7


Section Formula internally =


Where l = 2 and m = 7


A (–6, –5) and B (–6, 4)


=


=


=


= (–6, –3)


Therefore, the point P is (–6, –3).


More from this chapter

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6

Find the coordinates of the point which divides the line segment joining (3, 4) and (–6, 2) in the ratio 3: 2 externally.

 7

Find the coordinates of the point which divides the line segment joining (–3, 5) and (4, –9) in the ratio 1: 6 internally.

 9

Find the points of trisection of the line segment joining the points A (2, –2) and B (–7, 4).

 10

Find the points which divide the line segment joining A (–4 ,0) and B (0,6) into four equal parts.