Question

NEED HELP ASAP 30 POINTS WILL BE GIVEN TO BRAINLIEST

Answer 1

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$G(-1,3)\ H(1,2)\ J(-3,-1)$

Step 1

Find the slope GH

$G(-1,3)\ H(1,2)$

substitute in the formula

$m=\frac{2-3}{1+1}$

$m=\frac{-1}{2}$

$mGH=-\frac{1}{2}$

Step 2

Find the slope HJ

$H(1,2)\ J(-3,-1)$

substitute in the formula

$m=\frac{-1-2}{-3-1}$

$m=\frac{-3}{-4}$

$mHJ=\frac{3}{4}$

Step 3

Find the slope JG

$J(-3,-1)\ G(-1,3)$

substitute in the formula

$m=\frac{3+1}{-1+3}$

$m=\frac{4}{2}$

$mJG=2$

Step 4

Verify if triangle GHJ is a right triangle

we know that

if two lines are perpendicular, then the product of their slopes is equal to minus one

so

$m1*m2=-1$

compare slope GH with slope JG

we have

$mGH=-\frac{1}{2}$

$mJG=2$

$-\frac{1}{2}*2=-1$ -----> side GH and side JG are perpendicular

The triangle GHJ is a right triangle

The answer in the attached figure