Question

What is the area of a triangle whose vertices are

R(−4, 2),S(1, 2), and T(−5, −4)?
 
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Answer 1

15 units

Explanation:

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Answer 2

ANSWER

15 square units.

EXPLANATION

This triangle has one of its height(altitudes) falling outside the triangle.

We determine the base using absolute value method. This is because the coordinates of
`R(-4,2)` and
`S(1,2)` tell us that this line is horizontal. The y-values are constant.

Therefore
`|RS|=|1--4|`


`\Rightarrow |RS|=|1+4|`


`\Rightarrow |RS|=|5|`


`\Rightarrow |RS|=5`

Also

The triangle is bounded between
`y=2` and
`y=-4`.

Therefore the vertical height of interest,


`|RT|=|-4-2|`


`|RT|=|-6|`


`|RT|=6`

We can now find the area using the formula


`Area=(1)/(2)base* height`


`Area=(1)/(2)*6 * 5`


`Area=3 * 5`


`Area=15` square units