The slope of line AB is
slope = (change in y)/(change in x)
slope = (14 -(-3))/(7 -(-10)) = 17/17 = 1
The slope of line CD is the negative reciprocal of that, -1/1 = -1.
The point-slope form of the equation for line CD can be written as
y = -1(x -5) +12
y = -x +17
The x-intercept is the value of x when y = 0.
0 = -x +17
x = 17
The x-intercept is ...
(17, 0)
Another way to write the equation for line CD is "standard form." For this, we add x to the slope-intercept form to get ...
x + y = 17
For the second part of your question, we can find the answer by adding the x- and y-coordinates to see which sum is 17.
-5 +24 = 19
-2 +19 = 17 . . . . . . . . . the point (-2, 19) is the correct choice
7 +(-10) = -3
8 +11 = 19
