Question

(I'm having to do plato, and I have NO idea how to do any of it. I'm just trying to pass. They never taught us any of this in Geometry, and I'm clueless. )
CD is perpendicular to AB and passes through point C(5, 12).
If the coordinates of A and B are (-10, -3) and (7, 14), respectively, the x- intercept of CD is ___ . The point ___ lies on CD.

Answer 1

Drawing always helps me understand a problem better.



It is a rough drawing and I suspect that point C is actually on like AB, but it gives me a more visual idea of what is going on.

Answer 2

best to find the equation of the line CD using the point C and the fact that it is perpendicular to AB. Use gradients - remember m1 x m2 = -1 if the lines are perpendicular to each other

Gradient of AB = \[mAB = \frac{ 14-(-3) }{ 7-(-10) } = \frac{ 17 }{17 } = 1\]
so gradient of CD = -1/mAB = -1/1 = -1

Then sub in this gradient into the point gradient formula of the line with the it passes through being C(5,12)

y - y1 = m(x - x1)
y - 12 = -1(x - 5)

then find the x intercept by letting y = 0 and solving for x. This x intercept in then one of the points that lies on CD.

Answer 3

I think what they ware testing is your understanding of slope and the general equation of lines in a cartesian plane. Please reread your book or look online about that.

Slope is given by the formula
\[m=(y _{2}-y _{1})/(x _{2}-x _{1})\]
in the case of line AB
m=the slope of line AB, so point 2 is B (7,14) and point 1 is A (-10, -3) making the formula
m=(14-(10)/(7-(-3) = ?

So we know what the slope of AB is.
We also know what the slope of CD is since we are told it is perpindicular to AB. That means its slope is the negative inverse of AB.

All that is left to do is to find the x intercept which for line CD which is where y=0

Answer 4

My problem is, they taught us the very basics of geometry last year. None of this was covered. I've tried watching videos, but I'm the kind of person that comprehends the subject best when someone sits down with me and shows me. Which, I do not have access to because the education in Arkansas is.... not the best. But thank you to both of you for showing me how to solve it! I appreciate it a lot. @plainntall @mww