Question

Calculate the area of triangle QRS with altitude ST, given Q (0, 5), R (−5, 0), S (−3, 4), and T (−2, 3).

A- 6.2 square units

B- 7 square units

C- 5.9 square units

D- 5 square units

Answer 1

The correct answer among the choices provided is option D. The area of triangle QRS with altitude ST is 5 square units. To solve for the area, the distance formula was used. The formula was substituted with the given values, QR=√[(-5-0)²+(0-5)²].

Answer 2

we have that

$Q (0, 5)\\R (-5, 0)\\S (-3, 4)\\T (-2, 3)$

using a graph tool

see the attached figure

the Area of triangle QRS is equal to

$A=\frac{1}{2}*b*h\\ A=\frac{1}{2}*RQ*ST$

1) Find the distance RQ

Applying the formula of distance

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

$dRQ=\sqrt{(0-5)^{2}+(-5-0)^{2}}$

$dRQ=\sqrt{(25)+(25)}$

$dRQ=\sqrt{50} units$

2) Find the distance ST

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

$dST=\sqrt{(1)+(1)}$

$dST=\sqrt{2} units$

3) Find the area of triangle QRS

$A=\frac{1}{2}*RQ*ST\\\\ A=\frac{1}{2}*\sqrt{50}*\sqrt{2} \\\\ A=\frac{1}{2}*\sqrt{100} \\ \\ A=\frac{10}{2} \\ \\ A=5 units^{2}$

therefore

the answer is the option

D- $5$ square units