Question

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:

(12, 0)
(15, 0)
(17, 0)
or (19,0).

The point:

(-5, 24)
(-2, 19)
(7, -10)
or (8, 11)

lies on CD.

Answer 1

CD is 17,0

The point -2,19

Explanation:

Answer 2

The slope of AB is

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`=(14-(-3))/(7-(-10))`

`=(17)/(17)`

`=1`

So the slope of CD is

`-(1)/(m)=-(1)/(1)=-1`

The equation for CD is then

`y=-x+b`
We find
`b` by plugging in the point
`(5, 12)`:

`12=-5+b`

`\rightarrow b=17`

`\rightarrow y=-x+17`

The x-intercept is found by setting
`y` equal to 0:

`0=-x+17`

`\rightarrow x=17`
which gives
`(17, 0)`.

For the second part, we just plug in the different points and see if the equation is true:

`(-5, 24)\rightarrow 24=-(-5)+17\rightarrow 24=5+17\rightarrow 24=22`
(doesn't work)

`(-2, 19)\rightarrow 19=-(-2)+17\rightarrow 19=2+17\rightarrow 19=19`
So the answer must be
`(-2, 19)`.