Answer:
Given that the points \[A(x,y),\,B(-5,7)\]and \[C(-4,5)\] are collinear. So, the area formed by the vertices are 0. Therefore, \[\frac{1}{2}[{{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}})]=0\] \[\Rightarrow \frac{1}{2}[x(7-5)-5(5-y)-4(y-7)]=0\] \[\Rightarrow \frac{1}{2}[x(2)-5(5-y)-4(y-7)]=0\] \[\Rightarrow 2x-25+5y-4y+28=0\] \[\Rightarrow 2x+y+3=0\] \[-2x-3=y\] which is the required, relation between x and y i.e., \[y=-2x-3\].
You need to login to perform this action.
You will be redirected in
3 sec