Question

The distance between the points (2, 7) and (k, -5) is 13. What is the value of k?

A) -7 B) 7 C) 6 D) -6

Answer 1

Step-by-step explanation:

Concept:

Distance formula: The distance between the two points A(x1, y1) and B(x2,y2) is given by

AB= Square root of { (x2-x1)²+ (y2-y1)²}

Solving:

Let A(2,7) and B(k,-5) be the given points.

Given,

Distance, AB= 13 units

or, Square root of { (k - 2 )²+ (- 5- 7)²} = 13

or, [Square root of { (k - 2 )²+ (- 5- 7)²}]² = (13)²

(Squaring both the sides)

or, k²- 4k + 4 + 144 = 169

{ Using formula: a²-2ab+b²= (a+b)²}

or, k²- 4k = 25

or, k²- 4k -25 = 0

or, solving this quadratic in k using quadratic formula we get the value of k