Question

Segment BD is an altitude of triangle ABC. Find the area of the triangle.

Answer 1

Answer: The correct option is A, i.e., 7.5.

Explanation:

It is given that ABC is a triangle and BD is an altitude.

Since BD is an altitude, therefore the height of the triangle is BD and the base of the triangle is AC.

The distance formula to find the distance between two points is,

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

First, we find BD, where B(-1,4) and D(2,4).

$BD=\sqrt{(2+1)^2+(4-4)^2}=\sqrt{9} =3$

So, the height of the triangle is 3.

Now, we find the value of AC, where A(2,1) and C(2,6).

$AC=\sqrt{(6-1)^2+(2-2)^2}=\sqrt{25} =5$

So, the base of the triangle is 5.

The formula to find the area of a triangle is,

$A=\frac{1}{2}\times {\text{base}}\times {\text{height}}$

$A=\frac{1}{2}\times 5\times 3=\frac{15}{2}=7.5$

Therefore, the area of the triangle is 7.5 unit square and the correct option is A.

Answer 2

Answer:

A. 7.5

Step-by-step explanation:

In triangle ABC, BD is the altitude of the triangle which means BD is its height and AC is its base.

We know that B(-1,4) and D(2,4), therefore we can find height BD using the distance formula:

$Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

BD = $\sqrt{(2+1)^2+(4-4)^2}$ $= 3$

Now, we will find the base AC:

$AC = \sqrt{(6-1)^2+(2-2)^2} = 5$

Area of the triangle = 1/2 * base * height

Area of ABC = 1/2 * AC * BD = 1/2 * 5 * 3 = 7.5

Therefore, the area of ABC is 7.5.