Which point on x-axis is equal distance from bracket 5, 9 bracket close and minus 4, 6?
Answers
by finding mid point we can have our answer
mid pt. (x)=(x1 + x2)/2
x=5-4/2
x=1/2
mid pt. (y)=(y1+ y2)/2
y=9+6/2
y=15/2
Answer:
Point = ( 3,0 )
Step-by-step explanation:
Let the point on x axis be denoted as ( x,0 )
According to the question, Distance of x from ( 5,9 ) is equal to Distance from ( -4, 6 ). Therefore Applying Distance Formula we get,
⇒ √ ( 5 - x )² + ( 9 - 0 )² = √ ( x + 4 )² + ( 0 - 6 )²
Squaring on both sides, we cancel out the roots. Hence we get,
⇒ [ 25 + x² -10x ] + 81 = [ x² + 8x + 16 ] + 36
⇒ x² - 10x + 25 + 81 = x² + 8x + 16 + 36
⇒ x² - 10x + 106 = x² + 8x + 52
Cancelling out x² from both sides we get,
⇒ -10x + 106 = 8x + 52
⇒ 106 - 52 = 8x + 10x
⇒ 54 = 18x
⇒ x = 54/18 = 3
Therefore the point on the x-axis where the distance from ( 5,9 ) is equal to distance from ( -4,6 ) is ( 3,0 ).