Question

9. Find the value of x such that AB = BC, where the
coordinates of A, B and Care (-5, 2), (1, -2) and
(x, 4) respectively.​

Answer 1

Answer:

The answer will be x = -15 and 17

Step-by-step explanation:

Answer 2

The value of x may be -3 and 5

Step-by-step explanation:

given that AB = BC

then

coordinates of A, B and Care (-5, 2), (1, -2) and  (x, 4)

using distance formula

d= $\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}$

distance of AB = $\sqrt{(1+5)^2 +(-2-2)^2}$

= $\sqrt{(6)^2+(-4)^2}$

$\sqrt{36+16}\\ = \sqrt{52}$

distance of BC = $\sqrt{(x-1)^2 +(4+2)^2}$

= $\sqrt{(x-1)^2+(6)^2} = \sqrt{(x-1)^2+36}$

since AB = BC

$\sqrt{(x-1)^2+36} = \sqrt{52}$

squaring both sides

$(\sqrt{(x-1)^2+36})^2 = (\sqrt{52})^2$

(x-1)² +36 = 52

x²+1-2x = 16

x²-2x-15= 0

x²-5x+3x-15=0

x(x-5) +3(x-5)

(x-5) (x+3) = 0

x-5 = 0

x = 5

x+3= 0

x = -3

hence , The value of x may be -3 and 5

#Learn more:

if x+1/x=5, Find the values of-

A) x^2+1/x^2

B) x^4+1/x^4​

https://brainly.in/question/12558899