Question

What is the area of a triangle with vertices at (0, −2) , ​ (8, −2) ​ , and ​ (9, 1) ​ ?

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___ units²

Answer 1

check the picture below.

recall that A = 1/2 bh.

Answer 2

12 square units.

Explanation:

When we plot the points representing the vertices of this triangle, we see that we do not have a segment perpendicular to any side; this means we do not have a height. What we do have is a horizontal line segment from (0, -2) to (8, -2), a segment running diagonally from (0, -2) to (9, 1) and a segment running diagonally from (9, 1) to (8, -2).

In order to find the height, we can drop a vertical line segment from the highest point, (9, 1), straight down adjacent to our horizontal line segment. This will be perpendicular. It runs from (9, 1) to (9, -2); its length would be 1--2 = 3 units. This is the height.

We will treat the horizontal segment as the base of the triangle; its length is 8-0 = 8.

Our formula for the area of a triangle is

A = 1/2bh

Using our information, we have

A = 1/2(8)(3) = 4(3) = 12