# 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.

Q1:

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.

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.

Q3:

In the figure, the coordinates of points , , and are , , and , respectively. Determine the lengths of and , and then calculate the area of , where a unit length . • A, , area of
• B, , area of
• C, , area of
• D, , area of

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 .

Q8:

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. Q10:

Given that is an isosceles triangle, where the coordinates of the points , , and are , , and , find the area of .

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

Q19:

Given that is an isosceles triangle, where the coordinates of the points , , and are , , and , find the area of .

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