# Worksheet: Triangles on the Coordinate Plane

In this worksheet, we will practice finding the vertices, side lengths, perimeter, and area of a triangle on the coordinate plane.

**Q2: **

A triangle has vertices at the points , , and with coordinates , , and respectively. Work out the perimeter of the triangle . Give your solution to two decimal places.

**Q4: **

A triangle has vertices at the points , , and with coordinates , , and respectively. Work out the area of the triangle .

**Q5: **

A triangle has vertices at the points , , and with coordinates , , and respectively.

Work out the perimeter of the triangle . Give your solution to one decimal place.

By drawing a rectangle through the vertices of the triangle, or otherwise, work out the area of the triangle .

**Q6: **

Given that the vertices of are , , and , determine its perimeter, rounded to the nearest tenth, and then find its area.

- Aperimeter , area
- Bperimeter , area
- Cperimeter , area
- Dperimeter , area
- Eperimeter , area

**Q7: **

A triangle has vertices at the points , , and with coordinates , , and respectively.

Work out the perimeter of the triangle . Give your solution to two decimal places.

Work out the area of the triangle .

**Q9: **

Find the area of the following right triangle.

**Q11: **

Given that the coordinates of the points ,, and are , , and , respectively, determine the area of .

- A9square units
- B49.5square units
- C11square units
- D99square units

**Q12: **

A triangle is drawn in the coordinate plane with its vertices at , , and .

Find the length of the base .

Find the height of the triangle.

Hence, find the area of the triangle.

- A12.5 square units
- B25 square units
- C6.25 square units
- D10 square units
- E22.5 square units

**Q13: **

Find the area of the triangle given the line drawn from the point is perpendicular to the straight line passing through the points and . Give the answer to the nearest square unit.

- A39 square unit
- B22 square unit
- C78 square unit
- D19 square unit

**Q14: **

The quadrilateral is formed by the points , , , and . Calculate the length of .

**Q15: **

The vertices of quadrilateral are , , , and . Find the lengths of and .

- A,
- B,
- C,
- D,
- E,

**Q16: **

Find the area of the colored region.

**Q17: **

Given that the vertices of are , , and , determine its perimeter, rounded to the nearest tenth, and then find its area.

- Aperimeter , area
- Bperimeter , area
- Cperimeter , area
- Dperimeter , area
- Eperimeter , area

**Q18: **

Given that the coordinates of the points ,, and are , , and , respectively, determine the area of .

- A22.5square units
- B49.5square units
- C27.5square units
- D99square units

**Q20: **

Find the area of the following right triangle.

**Q21: **

Find the area of the following right triangle.

**Q22: **

Triangle has vertices , , and . Use vectors to determine the coordinates of the point of intersection of its medians.

- A
- B
- C
- D

**Q23: **

is a triangle in which the coordinates of , , and are , , and respectively. If is a median of the triangle, determine the equation of .

- A
- B
- C
- D

**Q24: **

If , , and are vertices of a triangle, find the coordinates of the point of intersection of its medians.

- A
- B
- C
- D

**Q25: **

is a right triangle at , and is its median from . Given and , find the coordinates of and the length of the median.

- A,
- B,
- C,
- D, 5