Question

$\triangle DEF$ is a right triangle with area $A$ and vertices $D(0,\ 0),\ E(a,\ b)$ , and $F(a,\ 0)$ . Point $G$ is the midpoint of $\overline{DE}$ , and point $H$ is the midpoint of $\overline{DF}$ . Write an expression for the area of $\triangle DGH$ . Expression: square units Question 2 Justify your answer.

Answer 1

The expression for the area of ΔDGH is ab/8

Writing an expression for the area of ΔDGH.

From the question, we have the following parameters that can be used in our computation:

D(0, 0), E(a, b), and F(a, 0) .

We know that

• Point G is the midpoint of DE
• Point H is the midpoint of DF

This means that

G = (0 + a, 0 + b)/2

G = (a/2, b/2)

H = (0 + a, 0 + 0)/2

H = (a/2, 0)

The area of the triangle is calculated using

Area = 1/2 * |x₁y₂ - x₂y₁ + x₂y₃ - x₃y₂ + x₃y₁ - x₁y₃|

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * |0 * b/2 - a/2 * 0 + a/2 * 0 + a/2 * b/2 - a/2 * 0 - 0 * 0|

This gives

Area = 1/2 * |0 - 0 + 0 + ab/4 - 0 - 0|

So, we have

Area = 1/2 * ab/4

Area = ab/8

Hence, the expression for the area is ab/8

Question

Δ DEF is a right triangle with area A and vertices D(0, 0), E(a, b), and F(a, 0) . Point G is the midpoint of DE , and point H is the midpoint of DF.

Write an expression for the area of ΔDGH.