Question

What is the area of ABC?

Answer 1

Answer:

Area of triangle ABC = 10

Option C is correct.

Step-by-step explanation:

We need to find area of triangle ABC

We are given A(2,1) B(4,7) and C(6,3)

The formula used to find $Area \ of \ triangle=\frac{1}{2}base\times height$ ABC is:

In the given triangle base= AC and height = BC

First we need to find the distance between A and C and B and C

The formula used to find distance between AC $Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

We have $x_1=2, y_1=1, x_2=6, y_2=3$

Putting values and finding distance

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(6-2)^2+(3-1)^2}\\Distance=\sqrt{(4)^2+(2)^2}\\Distance=\sqrt{16+4}\\Distance=\sqrt{20}$

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

We have $x_1=4, y_1=7, x_2=6, y_2=3$

Putting values and finding distance

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Distance=\sqrt{(6-4)^2+(3-7)^2}\\Distance=\sqrt{(2)^2+(4)^2}\\Distance=\sqrt{4+16}\\Distance=\sqrt{20}$

So, We have height = $\sqrt{20}$ and base = $\sqrt{20}$

Finding area of triangle

$Area \ of \ triangle=\frac{1}{2}base\times height\\Area \ of \ triangle=\frac{1}{2}\sqrt{20} \times \sqrt{20} \\Area \ of \ triangle=\frac{1}{2}\times 20\\Area \ of \ triangle=10$

So, Area of triangle ABC = 10

Option C is correct.