Select the correct answer from each drop-down menu.
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

include a picture of the drawing in order for me to

step-by-step explanation:

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.