Find x if the distance between
points L(5,-8) and M(x,-3) is 13
Answers
Answer:
12
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Answer:
x is -7 or 17
Step-by-step explanation:
L = x , y = 5 , -8
M = x₁ , y₁ = x . -3
Distance = 13 units
To find : x
Applying distance formula :
D = √( x - x₁ )² + ( y - y₁ )²
13 = √( 5 - x )² + ( -8 - (-3))²
Using identity ( a - b )² = a² + b² - 2ab
13 = √ 5² + x² - 2 * 5 * x + ( -8 + 3 )²
13 = √25 + x² - 10x + (-5)²
13 = √25 + x² - 10x + 25
13 = √50 + x² - 10x
Squaring both sides
169 = 50 + x² - 10x
169 = x² - 10x + 50
0 = x² - 10x + 50 - 169
0 = x² - 10x + 50 - 169
0 = x² - 10x - 119
Factorising x² - 10x - 119
0 = x² - 17x + 7x - 119
0 = ( x² - 17x ) + ( 7x - 119 )
0 = x ( x - `17 ) + 7 ( x - 17 )
0 = ( x - 17 ) ( x + 7 )
Either x - 17 or x + 7 = 0
x - 17 = 0 x + 7 = 0
x = 17 x = -7
x is 17 or -7