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