If CD is perpendicular on AB then the x intercept of CD is (17,0).
Given that CD is perpendicular on AB and passes through C(5,12) and the coordinates of A and B are (-10,-3), (7,14).
When two lines are perpendicular on other line then the product of their slopes is equal to -1.
It is given that CD is perpendicular on AB. So we need to first calculate the slope of AB.
Slope=[tex](y_{2} -y_{1} /x_{2} -x_{1} )[/tex]
Slope of AB=(14+3/7+10)
=(17/17)
=1
According to rule product of slopes of AB and CD should be -1.
So the slope of CD will be -1.
Now we have to form equation of CD from slope -1 and point (5,12).
y-12=-1(x-5)
y-12=-x+5
x+y-17=0
We have to find out x intercept.
We know that x intercept is a point where the line touches x axis. So here the value of y =0.
x+y-17=0
put the value of y=0.
x+0-17=0
x=17
Point will be (17,0)
Hence the x intercept of CD will be (17,0).
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Question is incomplete as it should include in its beginning that CD is perpendicular on AB.
