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Answer 1

$\huge\mathbb\pink{Answer }$

12) Let the line divides the points in k:1 ratio according to section formula

(2k+1/k+1, 7k+3/k+1) = (x, y)

It must satisfy the given equation so

3(2k+1/k+1) + (7k+3/k+1) = 9

6k+3+7k+3/k+1 = 9

13k+6=9k+9

13k-9k=9-6

4k=3

k=3/4.

13)Given P(2,2) is equidistance from the points

A(-2,k) and B(-2k,-3)

. ∴ PA = PB (Squaring on Both Sides)

PA2 = PB2 (- 2 - 2)2 + (k - 2)2 = (-2k - 2)2 + (-3 - 2)2

⇒ 16 + k2 + 4 - 4k = 4k2 + 4 + 8k + 25

⇒ 3k2 + 12k + 9 = 0

⇒ k2 + 4k + 3 = 0

⇒ k2 + 3k + k + 3 = 0

⇒ k(k + 3) + 1(k + 3) = 0

⇒ k + 1 = 0 and k + 3 = 0

k = -1, -3.

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