Question

1. triangle lmn is on a coordinate plane with its vertices located at l(-2, 0), m(4, -1), and n(4, 7). what is the area of δlmn?

Explanation:

Step1: Identify the base length

Points M(4, -1) and N(4, 7) have the same x - coordinate, so the length of MN is the difference in the y - coordinates.
Length of \(MN=\vert7 - (-1)\vert=\vert7 + 1\vert = 8\)

Step2: Identify the height

The base MN is a vertical line (since x - coordinate is constant). The height is the horizontal distance from point L(-2, 0) to the line x = 4.
The horizontal distance (height) \(h=\vert4-(-2)\vert=\vert4 + 2\vert=6\)

Step3: Calculate the area of the triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\)
Substitute base = 8 and height = 6 into the formula:
\(A=\frac{1}{2}\times8\times6\)
First, \(\frac{1}{2}\times8 = 4\), then \(4\times6=24\)

Answer:

24