Q10 of 84 Page 114

If the distance between two points (x,7) and (1, 15) is 10, find x.

Formula used:


Given: Distance = 10 and coordinates of two points is A (x, 7) and B (1, 15)


AB = √ (x2 – x1)2 + (y2 – y1)2


⇒ 10 = √ (1 – x)2 + (15 – 7)2


⇒ 10 = √ (1 – x)2 + 82


Squaring both sides


⇒ 102 = (1 – x)2 + 82


⇒ 100 = 1 – 2x + x2 + 64


⇒ 100 = x2 – 2x + 65


⇒ x2 – 2x + 65 – 100 = 0


⇒ x2 – 2x – 35 = 0


⇒ x2 – 7x + 5x – 35 = 0


⇒ x (x – 7) + 5(x – 7) = 0


⇒ (x – 7) (x + 5) = 0


x – 7 = 0 or x + 5 = 0


x = 7 or x = –5


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