Question

Calculate the area of triangle ABC with altitude CD, given A(−7, −1), B(−1, 5), C(0, 0), and D(−3, 3). 9 square units 18 square units 18.5 square units 21 square units

Answer 1

Use the distance formula which is root( (x2-x1) ^2+(y2-y1)^2). Find the length of base AB which will come out to be 6root2 units and the height CD which is equal to 3root2 units. So, area is 0.5*b*h=0.5*18*2=18 Sq units.

Answer 2

Answer:

The area of the triangle is 18 sq units.

Step-by-step explanation:

The given values are A (−7, −1), B (−1, 5), C (0, 0), and D (−3, 3), and we need to calculate the area of triangle ABC which has CD as the altitude.

AB = $\sqrt{-7+1+(-1-5)^{2}}$

= √(36+36)

= √72

= 6√2

CD = $\sqrt{(0+3)^{2}+(0-3)^{2}}$

= √(9+9)

= √18

= 3√2

The formula for the area of triangle is ½ x base x altitude.

Now, by substituting the given values in the above formula, we get the following result.

Area of triangle = 1/2 x 6√2 x 3√2

= 1/2 x 18 x 2

= 18 sq units.