Question

40 POINTS NEED HELP ASAP

Answer 1

Use slope formula: y2-y1/x2-x1

XZ: -5/9
YZ: 2/7
XY: -7/2

XYZ is a right triangle because two of these slopes have a product of -1.

(YZ and XY does).  We are all busy these days.

Answer 2

we know that

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

so

$m1*m2=-1$

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

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

we have

$x(-5,5)\\y(-3,-2)\\z(4,0)$

Step 1

Find the slope xz

$x(-5,5)\\z(4,0)$

Substitute in the slope's formula

$m=\frac{(0-5)}{(4+5)}$

$m=\frac{(-5)}{(9)}$

$mxz=-\frac{5}{9}$

Step 2

Find the slope yz

$y(-3,-2)\\z(4,0)$

Substitute in the slope's formula

$m=\frac{(0+2)}{(4+3)}$

$m=\frac{(2)}{(7)}$

$myz=\frac{2}{7}$

Step 3

Find the slope xy

$x(-5,5)\\y(-3,-2)$

Substitute in the slope's formula

$m=\frac{(-2-5)}{(-3+5)}$

$m=\frac{(-7)}{(2)}$

$mxy=-\frac{7}{2}$

Step 4

Verify if two of the slopes are perpendicular

$mxz=-\frac{5}{9}$

$myz=\frac{2}{7}$

$mxy=-\frac{7}{2}$

Multiply  myz and mxy

$\frac{2}{7}*-\frac{7}{2}=-1$ -------> the lines segment yz and xy are perpendicular

therefore

the triangle XYZ is a right triangle    

the answer in the attached figure