### Finding the Area of a Triangle on a Coordinate Plane**Problem:**What is the area of the triangle with vertices $ L(-3, 5) $, $ M(4, 7) $, and $ N(2, -8) $? Use any method to find the answer.**Graph Description:**The graph provided shows a coordinate plane with a triangle outlined. The vertices of the triangle are marked as follows:- $ L $ at coordinates $(-3, 5)$- $ M $ at coordinates $(4, 7)$- $ N $ at coordinates $(2, -8)$The x-axis and y-axis intersect at the origin $(0, 0)$. The grid lines are labeled incrementally with numbers, both positive and negative.**Options:**- 25.5 square units.- 57.5 square units.- 45.5 square units.- 50.5 square units.**Method:**To find the area of a triangle given its vertices, you can use the formula:\[\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|\]Substitute the coordinates of $ L(-3, 5) $, $ M(4, 7) $, and $ N(2, -8) $:- $ x_1 = -3 $, $ y_1 = 5 $- $ x_2 = 4 $, $ y_2 = 7 $- $ x_3 = 2 $, $ y_3 = -8 $Calculate the area:\[\begin{align*}\text{Area} &= \frac{1}{2} \left| (-3)(7 - (-8)) + 4((-8) - 5) + 2(5 - 7) \right| \\&= \frac{1}{2} \left| (-3)(15) + 4(-13) + 2(-2) \right| \\&= \frac{1}{2} \left| (-45) + (-52) + (-4) \right| \\&

Name: ### Finding the Area of a Triangle on a Coordinate Plane**Problem:**W
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Description: ### Finding the Area of a Triangle on a Coordinate Plane**Problem:**What is the area of the triangle with vertices $ L(-3, 5) $, $ M(4, 7) $, and $ N(2, -8) $? Use any method to find the answer.**Graph Description:**The graph provided shows a

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Answered: What is the area of the tranglo with…

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What is the area of the tranglo with vertices L (-3, 5). M (4, 7). and N (2, –-8)? Uso any method to find the ans answer. 25.5 square units. 57.5 square units. 45.5 square units. 50.5 square units.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

### Finding the Area of a Triangle on a Coordinate Plane

**Problem:**
What is the area of the triangle with vertices $ L(-3, 5) $, $ M(4, 7) $, and $ N(2, -8) $? Use any method to find the answer.

**Graph Description:**
The graph provided shows a coordinate plane with a triangle outlined. The vertices of the triangle are marked as follows:
- $ L $ at coordinates $(-3, 5)$
- $ M $ at coordinates $(4, 7)$
- $ N $ at coordinates $(2, -8)$

The x-axis and y-axis intersect at the origin $(0, 0)$. The grid lines are labeled incrementally with numbers, both positive and negative.

**Options:**
- 25.5 square units.
- 57.5 square units.
- 45.5 square units.
- 50.5 square units.

**Method:**
To find the area of a triangle given its vertices, you can use the formula:

\[
\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|
\]

Substitute the coordinates of $ L(-3, 5) $, $ M(4, 7) $, and $ N(2, -8) $:
- $ x_1 = -3 $, $ y_1 = 5 $
- $ x_2 = 4 $, $ y_2 = 7 $
- $ x_3 = 2 $, $ y_3 = -8 $

Calculate the area:

\[
\begin{align*}
\text{Area} &= \frac{1}{2} \left| (-3)(7 - (-8)) + 4((-8) - 5) + 2(5 - 7) \right| \\
&= \frac{1}{2} \left| (-3)(15) + 4(-13) + 2(-2) \right| \\
&= \frac{1}{2} \left| (-45) + (-52) + (-4) \right| \\
&

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