Question

6. If the point A(x, 2) is equidistant from the points B(8, -2) and C(2,-2),
find the value of x. Also, find the length of AB.
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Answer 1

Answer:

x = 5

length of AB is 25

Step-by-step explanation:

AB = AC

The distance point formula is

c2 = (xA − xB)2 + (yA − yB)2

$\sqrt{(x - 8) { } ^{2} +( 2 - ( - 2) ) { }^{2} } = \sqrt{(x - 2) {}^{2} + 2 - ( - 2)} )$

Squaring on both sides, we get

(x - 8)² + (2+2)² = ( x - 2)² + (2 + 2)²

x² - 16x + 64 + 16 = x² -4x + 4 + 16

x² -16x + 64 + 16 - x² +4x + 4 - 16 = 0

-12x + 60 = 0

- 12 ( x - 5) = 0

x - 5 = 0

X = 5

The length of AB is

$ab = \sqrt{(5 - 8) {} ^ {2} + (2 - ( - 2)) {}^{2} }$

Squaring on both sides we get ,

AB = (-3)² + 4²

= 9 + 16

= 25