Parker threw a ball from a window whose location is at (13,5). The ball touched the ground and bounced forward making an angle of 90 degrees with the line segment connecting the coordinates of the window and the point where the ball touched the ground. Fatima caught the ball whose current location is at (0,8). What will be the x-coordinate of the point on the ground where the ball touches? Consider the ground to be on the X-axis.
Answers
Given : Parker threw a ball from a window whose location is at (13,5).
The ball touched the ground and bounced forward making an angle of 90 degrees with the line segment connecting the coordinates of the window and the point where the ball touched the ground.
Fatima caught the ball whose current location is at (0,8).
Consider the ground to be on the X-axis.
To Find: the x-coordinate of the point on the ground where the ball touches
Solution:
the x-coordinate of the point on the ground where the ball touches = x
as point is in x axis hence y coordinate = 0
so point will be (x , 0)
Slope of line segment joining point (x , 0) and ( 13 , 5)
= (x - 13)/(0 - 5)
= (x - 13)/(-5)
= (13 - x)/5
Slope of line segment joining point (x , 0) and ( 0 , 8)
= (x - 0)/(0 - 8)
= x/(-8)
= -x/8
As line segments are perpendicular hence product of their slopes will be -1.
{(13 - x)/5} * {-x/8} = - 1
=> x(13 - x) = 40
=> 13x - x² = 40
=> x² - 13x + 40 = 0
=> (x - 5)(x - 8) = 0
=> x = 5 , 8
x-coordinate of the point on the ground where the ball touches can be
( 5 , 0 ) or ( 8 , 0)
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