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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.

Solution:

CD is perpendicular to AB and passes through point C(5, 12)

Coordinates of A and B are (-10, -3) and (7, 14)

Find slope of AB

From given,

Substituting we get,

CD is perpendicular to AB

We know that,

Product of slope of AB and slope of line CD which is perpendicular to AB is equal to -1

Therefore,

The equation of CD in slope intercept form is:

y = mx + c --------- eqn 1

Where,

m is the slope

c is the y intercept

Substitute m = -1 and (x, y) = (5, 12) in eqn 1

12 = -1(5) + c

c = 12 + 5

c = 17

Substitute m = -1 and c = 17 in eqn 1

y = -x + 17 ------ eqn 2

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

0 = -x + 17

x = 17

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

Substitute (x, y) = (-5, 24) in eqn 2

Thus, Point (-2, 19) lies on CD

19

step-by-step explanation: