Question

Is perpendicular to 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 is
. The point
lies on .

Answer 1

Step-by-step explanation:

To find the x-intercept of the line passing through point C(5,12) and perpendicular to the line passing through points A(-10,-3) and B(7,14), we first need to find the equation of the line passing through points A and B.

The slope of the line passing through points A and B is:

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

m = 17 / 17

m = 1

So, the equation of the line passing through points A and B can be written as:

y - (-3) = 1(x - (-10))

y + 3 = x + 10

y = x + 7

The line perpendicular to this line will have a slope of -1 (negative reciprocal of 1).

So, the equation of the line passing through point C(5,12) and perpendicular to the line passing through points A and B can be written as:

y - 12 = -1(x - 5)

y - 12 = -x + 5

y = -x + 17

To find the x-intercept, we can set y = 0 in this equation and solve for x:

0 = -x + 17

x = 17

Therefore, the x-intercept of the line passing through point C(5,12) and perpendicular to the line passing through points A(-10,-3) and B(7,14) is x = 17.

To find the point on which the x-intercept lies, we can substitute x = 17 into the equation of the line passing through points A and B:

y = x + 7

y = 17 + 7

y = 24

So, the point on which the x-intercept lies is (17,24).