Respuesta :
x intercept of CD is (17, 0)
Point (-2, 19) 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
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
From given,
[tex](x_1, y_1) = (-10 , -3)\\\\(x_2, y_2) = (7, 14)[/tex]
Substituting we get,
[tex]m = \frac{14+3}{7+10}\\\\m = \frac{17}{17}\\\\m = 1[/tex]
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,
[tex]1 \times \text{ slope of CD } = -1\\\\\text{ slope of CD } = -1[/tex]
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
Thus x intercept of CD is (17, 0)
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
[tex](-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[/tex]
Thus, Point (-2, 19) lies on CD
Answer:
x intercept of CD is (17, 0)
Point (-2, 19) lies on CD
