Question

(05.01 MC)

Which statement best describes the area of Triangle ABC shown below?

A triangle ABC is shown on a grid. The vertex A is on ordered pair 4 and 5, vertex B is on ordered pair 5 and 2, and the vertex C is on ordered pair 3 and 2.

It is one-half the area of a rectangle with sides 2 units × 3 units.
It is twice the area of a rectangle with sides 2 units × 3 units.
It is one-half the area of a square of side length 3 units.
It is twice the area of a square of side length 3 units.

Answer 1

It is one-half the area of a rectangle with sides 2 units × 3 units.

Explanation:

Answer 2

It is one-half the area of a rectangle with sides 2 units × 3 units.

Explanation:

we have the coordinates of triangle ABC

A(4,5),B(5,2),C(3,2)

Plot the coordinates of triangle to better understand the problem

see the attached figure

step 1

Find the area of triangle ABC

The triangle ABC is an isosceles triangle `(AB=AC)

The area of triangle ABC is

`A=(1)/(2)(BC)(AM)`

we have

`BC=5-3=2\ units` ---> difference of the x-coordinates

`AM=5-2=3\ units` ---> difference of the y-coordinates

substitute

`A=(1)/(2)(2)(3)=3\ units^2`

step 2

Find one-half the area of a rectangle with sides 2 units × 3 units

`A=(1)/(2) (2)(3)=3\ units^2`

therefore

The area of triangle ABC is one-half the area of a rectangle with sides 2 units × 3 units