Question

(WILL MARK AS BRAINLIEST) Consider the graph of quadrilateral WXYZ.

Answer 1

The first, third, fifth, and last one are right. Do you want me to show you the steps or are u good

Answer 2

Answer:

The slope of ZW is $\frac{2}{5}$

The lenght of ZY is $\sqrt{29}$

Quadrilateral WXYZ is a square

Step-by-step explanation:

Statements

case A) The slope of ZW is $\frac{2}{5}$

The statement is True

we know that

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

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

we have

$Z(-3,1),W(2,3)$

substitute

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

$m=\frac{2}{5}$

case B) The slope of YX is $-\frac{5}{2}$

The statement is False

we know that

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

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

we have

$Y(-1,-4),X(4,-2)$

substitute

$m=\frac{-2+4}{4+1}$

$m=\frac{2}{5}$

case C) The lenght of ZY is $\sqrt{29}$

The statement is True

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

$Z(-3,1),Y(-1,-4)$

substitute

$d=\sqrt{(-4-1)^{2}+(-1+3)^{2}}$

$d=\sqrt{(-5)^{2}+(2)^{2}}$

$d=\sqrt{29}\ units$

case D) The lenght of WX is $5$

The statement is False

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

$W(2,3),X(4,-2)$

substitute

$d=\sqrt{(-2-3)^{2}+(4-2)^{2}}$

$d=\sqrt{(-5)^{2}+(2)^{2}}$

$d=\sqrt{29}\ units$

case E) Quadrilateral WXYZ is a square

The statement is True

Because  sides ZW and YX are parallel sides (has the same slope)

Slope ZY

we have

$Z(-3,1),Y(-1,-4)$

$m=\frac{-4-1}{-1+3}$

$m=-\frac{5}{2}$

so

ZW and ZY are perpendicular sides (the product of their slopes is equal to minus one)

$-\frac{5}{2}*\frac{2}{5}=-1$

Slope WX

we have

$W(2,3),X(4,-2)$

$m=\frac{-2-3}{4-2}$

$m=-\frac{5}{2}$

ZY and WX are parallel sides (has the same slope)

distance ZW

we have

$Z(-3,1),W(2,3)$

$d=\sqrt{(3-1)^{2}+(2+3)^{2}}$

$d=\sqrt{(2)^{2}+(5)^{2}}$

$d=\sqrt{29}\ units$

distance YX

we have

$Y(-1,-4),X(4,-2)$

$d=\sqrt{(-2+4)^{2}+(4+1)^{2}}$

$d=\sqrt{(2)^{2}+(5)^{2}}$

$d=\sqrt{29}\ units$

The four sides are congruent

case F) $YZ=\sqrt{(-3-(-1))^{2}+(1-4)^{2}}$

The statement is False

$YZ=\sqrt{(-2)^{2}+(-3)^{2}}$

$YZ=\sqrt{13}$  ----> is not correct

the value of YZ is  $\sqrt{29}$