find the value of x such that AB=BC where coordinates of A,B and C are (5,-2),(1,-2) and (x,4) respectively
Answers
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}
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
distance of AB = \sqrt{(1+5)^2 +(-2-2)^2}
(1+5)
2
+(−2−2)
2
= \sqrt{(6)^2+(-4)^2}
(6)
2
+(−4)
2
\begin{gathered}\sqrt{36+16}\\ = \sqrt{52}\end{gathered}
36+16
=
52
distance of BC = \sqrt{(x-1)^2 +(4+2)^2}
(x−1)
2
+(4+2)
2
= \sqrt{(x-1)^2+(6)^2} = \sqrt{(x-1)^2+36}
(x−1)
2
+(6)
2
=
(x−1)
2
+36
since AB = BC
\sqrt{(x-1)^2+36} = \sqrt{52}
(x−1)
2
+36
=
52
squaring both sides
(\sqrt{(x-1)^2+36})^2 = (\sqrt{52})^2(
(x−1)
2
+36
)
2
=(
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
Step-by-step explanation:
AB=BC
(5-2)(1-2) (*4)
3*1=3
3*4= 12
12*12=144