The slope of AB is \(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) \(=\frac{14-(-3)}{7-(-10)}\) \(=\frac{17}{17}\) \(=1\)
So the slope of CD is \(-\frac{1}{m}=-\frac{1}{1}=-1\)
The equation for CD is then \(y=-x+b\) We find \(b\) by plugging in the point \((5, 12)\): \(12=-5+b\) \(\rightarrow b=17\) \(\rightarrow y=-x+17\)
The x-intercept is found by setting \(y\) equal to 0: \(0=-x+17\) \(\rightarrow x=17\) which gives \((17, 0)\).
For the second part, we just plug in the different points and see if the equation is true: \((-5, 24)\rightarrow 24=-(-5)+17\rightarrow 24=5+17\rightarrow 24=22\) (doesn't work) \((-2, 19)\rightarrow 19=-(-2)+17\rightarrow 19=2+17\rightarrow 19=19\) So the answer must be \((-2, 19)\).
