Answer:
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).