Question

3 a triangular coral section is place in a tank with vertices at e(2,3), f(6,3), g(4,7). use the coordinate plane to find the area of the triangle, $a = \frac{1}{2}bh$: a 6 units² b 8 units² c 12 units² d 10 units²

Explanation:

Step1: Find the base length

The points E(2,3) and F(6,3) have the same y - coordinate. The base length $b$ is the difference in their x - coordinates. So $b=\vert6 - 2\vert=4$.

Step2: Find the height

The height $h$ is the perpendicular distance from the point G(4,7) to the line segment EF. Since EF is a horizontal line (y = 3), the height is the difference in the y - coordinates of G and any point on EF. So $h=\vert7 - 3\vert = 4$.

Step3: Calculate the area

Using the formula $A=\frac{1}{2}bh$, substitute $b = 4$ and $h = 4$. Then $A=\frac{1}{2}\times4\times4=8$.

Answer:

B. 8 units²