Question

question 15 (multiple choice worth 4 points) calculate the area of triangle cde with altitude ef, given c (3, -2), d (-1, 2), e (2, 3), and f (0, 1). 4 square units 6.2 square units 8 square units 8.7 square units

Explanation:

Step1: Calculate length of base CD

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $C(3,-2)$ and $D(-1,2)$, we have $x_1 = 3,y_1=-2,x_2=-1,y_2 = 2$. Then $CD=\sqrt{(-1 - 3)^2+(2+2)^2}=\sqrt{(-4)^2+4^2}=\sqrt{16 + 16}=\sqrt{32}=4\sqrt{2}$.

Step2: Calculate length of altitude EF

For points $E(2,3)$ and $F(0,1)$, using distance formula $EF=\sqrt{(0 - 2)^2+(1 - 3)^2}=\sqrt{(-2)^2+(-2)^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}$.

Step3: Calculate area of triangle

The area of a triangle $A=\frac{1}{2}\times base\times height$. Here base is $CD$ and height is $EF$. So $A=\frac{1}{2}\times4\sqrt{2}\times2\sqrt{2}=\frac{1}{2}\times16 = 8$.

Answer:

8 square units