Question

he area of triangle in the coordinate plane
which statement is true of the right triangles abc and def?
area of abc is equal to the area of def.
there is not enough information to compare the areas of triangles abc and def.
area of abc is less than area of def.
area of abc is greater than area of def.

Explanation:

Step1: Calculate the area of triangle \(ABC\)

The formula for the area of a right - triangle is \(A=\frac{1}{2}\times base\times height\). For triangle \(ABC\), assume \(AB = 6\) units (vertical side) and \(AC=10\) units (horizontal side). Then \(A_{ABC}=\frac{1}{2}\times6\times10 = 30\) square units.

Step2: Calculate the area of triangle \(DEF\)

For triangle \(DEF\), assume \(DF = 6\) units (vertical side from \(y = 8\) to \(y = 2\)) and \(EF = 10\) units (horizontal side from \(x=4\) to \(x = 14\)). Then \(A_{DEF}=\frac{1}{2}\times6\times10=30\) square units.

Answer:

Area of \(ABC\) is equal to the area of \(DEF\)