Question

If A is (1,2), B is (1,-6), and C is (4,7), what is the area of the triangle ABC?

Answer 1

Find the lengths of segments AB, BC, and CA then use Heron's Formula.

Answer 2

Could you please show me how to do that?

Answer 3

You have to first plot the points on an xy plane. It is best for you to familiarize yourself with a graphing program like http://www.desmos.com for plotting points, segments and lines.

Answer 4

Ok, then how do you find the length of the segments?

Answer 5

Hang on a minute....

Answer 6

Here's the triangle
https://www.desmos.com/calculator/w6m2pzx6a2

Answer 7

You can use distance formula to find the lengths of the segments.

Answer 8

If you click "Projector Mode" you would be better able to keep track of the units.

Answer 9

Obviously since the blue segment is completely vertical, it is easy to figure out its unit length of 8 units.

Answer 10

The unit length of the green segment is,
\[\sqrt{5^2 + 3^2} = \sqrt{25 + 9} = \sqrt{34}\]

Answer 11

The unit length of the purple segment is
\[\sqrt{13^2 + 3^2} = \sqrt{169 + 9} = \sqrt{178}\]

Answer 12

So now you have triangle segment lengths of \(8, \sqrt{34}, \sqrt{178}\)

Answer 13

Now use Heron's Formula to find the Area of the triangle.