Question

I need help on this FAST

Answer 1

Answer:

Area approximately equals 26.26 square units.

Step-by-step explanation:

All you need to do is use distance formula to find the length of line segment PT and line segment RQ.

D=√(X2-X1)^2+(Y2-Y1)^2

Plug the coordinates into the formula for each line segment

It doesn't matter what order you put the points into as long as you know which point is which ( which is (X1,Y1) and which is (X2,Y2) )

You can look at the picture of my work if you're still confused.

Answer 2

Answer:

$\large \boxed{24.0}$

Step-by-step explanation:

The formula for the area of  triangle is

A = ½bh

In your triangle, b = QR and h = PT.

We can use Pythagoras' Theorem to find the lengths of these line segments.

1. Length of QR

Draw a point U at (-2, -5) and connect line segments QU and RU.

QU = 6 - (-2)  = 6 + 2 = 8

RU = -1 - (-5) = -1 + 5 = 4

$\begin{array}{rcl}QR^{2}& = &QU^{2} + RU^{2} \\& = & 8^{2} + 4^{2}\\& = & 64 + 16\\& = &80\\QR & = & \sqrt{80}\\& = & 4\sqrt{5}\\\end{array}$

2. Length of PT

Draw a point S at (4, -3) and connect line segments PS and ST.

PS = 2 - (-2.8)  = 2 + 2.8 = 4.8

ST = 4 - 1.6       = 2.4

$\begin{array}{rcl}PT^{2}& = &PS^{2} + ST^{2} \\& = & 4.8^{2} + 2.4^{2}\\& = & 23.04 + 5.76\\& = &28.80\\PT & = & \sqrt{28.80}\\& \approx & 5.366\\\end{array}$

3. Area of  triangle

$\begin{array}{rcl}A & = & \dfrac{1}{2} \times 4 \sqrt{5} \times 5.366\\& = &24.0\\\end{array}\\\text{The area of the triangle is \large \boxed{\mathbf{24.0}} }$