IXL | Area of triangles on the coordinate plane

Graph

△

with vertices

(

)

(

–

)

and

(

)

Coordinate plane graph with 4 quadrants, x-axis coordinates from -10 to 10, y-axis coordinates from -10 to 10.

What is the area of

△

Area

square units

ref_doc_title.

Learn with an example

question

Graph

△

with vertices

(

)

(

–

)

and

(

–

)

What is the area of

△

Area

square units

key idea

Area of a triangle:

Area

solution

To graph

△

draw line segments connecting the vertices

(

)

(

–

)

and

(

–

)

To find the area of

△

first find its base and height. Then, use the formula for the area of a triangle.

Step 1: Find the base.

Any side of the triangle can be the base, but

is the best choice. Since

(

)

and

(

–

)

have the same

-coordinate,

is a horizontal line. So, it is straightforward to calculate VW.

VW is the absolute value of the difference in the

-coordinates

(

)

and

(

–

)

So,

–

Step 2: Find the height.

The height of

△

is the length of the altitude between

(

–

)

and

Since

(

–

)

and

(

–

)

have the same

-coordinate,

the altitude lies on the vertical line,

So, the height is just

–

Step 3: Find the area.

Finally, plug the values of the base and height into the formula for the area of a triangle.

Area of a triangle

Plug in

and

(

)

(

)

Plug in

and

Multiply

324

Multiply

Simplify

162

Simplify

So, the area of

△

is 162 square units.

Looking for more? Try these:

Lesson: Area of triangles

Lesson: Coordinate plane

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Teacher tools

Work it out

Not feeling ready yet? These can help:

R.7Distance between two points

Lesson: Area of triangles

Lesson: Coordinate plane

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