Question

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Answer 1

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Answer 2

Answer:

Ans. of 6 question

Value of k is 7 or -3

Step-by-step explanation:

Given: A(k, -5) , B(2,7)

Distance between the pts. is 13 units

To find: Value of k

Solution:

By distance fromula

AB = √(x2-x1)^2 + ( y2- y1)^2

13 = √[2-k]^2 + [7-(-5)]^2

13 = √(2-k)^2 + (7+5)^2

13 = √(2-k)^2 + (12)^2

13 = √ [(2)^2 - 2(2)(k) + (k)^2] + 144

13 = √ 4 - 4k + k^2 + 144

13 = √ k^2 - 4k + 148

squaring oth sides

169 = k^2 - 4k + 148

169 - 148 = k^2 - 4k

21 = k^2 - 4k

k^2 - 4k - 21 = 0

by splitting middle term

k^2 - 7k + 3k - 21 = 0

k (k - 7) + 3(k - 7) =0

(k - 7) (k + 3) = 0

k - 7 =0 OR k + 3 = 0

k =7 OR. k = -3

Therefore, the value of k is 7 or -3 .

I hope this will help you...