Q:

NEED HELP ASAP 30 POINTS WILL BE GIVEN TO BRAINLIESTThe coordinates of the vertices of △GHJ are  G(−1, 3),  H(1, 2), and  J(−3, −1)Drag and drop the choices into each box to correctly complete the sentencesbeen trying to solve this but just don't get it I keep getting it wrong on my homework

Accepted Solution

A:
we know thatThe formula to calculate the slope between two points is equal to[tex]m=\frac{y2-y1}{x2-x1}[/tex]we have[tex]G(-1,3)\ H(1,2)\ J(-3,-1)[/tex]Step 1Find the slope GH[tex]G(-1,3)\ H(1,2)[/tex]substitute in the formula[tex]m=\frac{2-3}{1+1}[/tex][tex]m=\frac{-1}{2}[/tex][tex]mGH=-\frac{1}{2}[/tex]Step 2Find the slope HJ[tex]H(1,2)\ J(-3,-1)[/tex]substitute in the formula[tex]m=\frac{-1-2}{-3-1}[/tex][tex]m=\frac{-3}{-4}[/tex][tex]mHJ=\frac{3}{4}[/tex]Step 3Find the slope JG[tex]J(-3,-1)\ G(-1,3)[/tex]substitute in the formula[tex]m=\frac{3+1}{-1+3}[/tex][tex]m=\frac{4}{2}[/tex][tex]mJG=2[/tex]Step 4Verify if triangle GHJ is a right trianglewe know thatif two lines are perpendicular, then the product of their slopes is equal to minus oneso[tex]m1*m2=-1[/tex] compare slope GH with slope JGwe have[tex]mGH=-\frac{1}{2}[/tex][tex]mJG=2[/tex][tex]-\frac{1}{2}*2=-1[/tex] -----> side GH and side JG are perpendicularThe triangle GHJ is a right triangleThe answer in the attached figure