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 𝐴, 𝐵, and 𝐶 with coordinates (3,3), (1,3), and (7,6) respectively. Work out the perimeter of the triangle 𝐴𝐵𝐶. Give your solution to two decimal places.

Q2:

A triangle has vertices at the points 𝐴, 𝐵, and 𝐶 with coordinates (2,2), (1,7), and (3,1) respectively. Work out the perimeter of the triangle 𝐴𝐵𝐶. Give your solution to two decimal places.

Q3:

In the figure, the coordinates of points 𝐴, 𝐵, and 𝐶 are (6,3), (8,3), and (6,7), respectively. Determine the lengths of 𝐴𝐶 and 𝐴𝐵, and then calculate the area of 𝐴𝐵𝐶, where a unit length =1cm.

  • A 𝐴 𝐶 = 4 c m , 𝐴 𝐵 = 2 c m , area of 𝐴𝐵𝐶=4cm
  • B 𝐴 𝐶 = 4 c m , 𝐴 𝐵 = 2 c m , area of 𝐴𝐵𝐶=8cm
  • C 𝐴 𝐶 = 2 c m , 𝐴 𝐵 = 4 c m , area of 𝐴𝐵𝐶=8cm
  • D 𝐴 𝐶 = 2 c m , 𝐴 𝐵 = 4 c m , area of 𝐴𝐵𝐶=4cm

Q4:

A triangle has vertices at the points 𝐴, 𝐵, and 𝐶 with coordinates (0,1), (0,2), and (5,0) respectively. Work out the area of the triangle 𝐴𝐵𝐶.

Q5:

A triangle has vertices at the points 𝐴, 𝐵, and 𝐶 with coordinates (2,1), (3,3), and (6,1) respectively.

Work out the perimeter of the triangle 𝐴𝐵𝐶. 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 𝐴𝐵𝐶.

Q6:

Given that the vertices of 𝑃𝑄𝑅 are 𝑃(0,3), 𝑄(1,4), and 𝑅(3,4), determine its perimeter, rounded to the nearest tenth, and then find its area.

  • Aperimeter =12, area =28
  • Bperimeter =18.1, area =24.75
  • Cperimeter =12, area =14
  • Dperimeter =18.7, area =28
  • Eperimeter =18.7, area =14

Q7:

A triangle has vertices at the points 𝐴, 𝐵, and 𝐶 with coordinates (0,5), (1,2), and (2,2) respectively.

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

Work out the area of the triangle 𝐴𝐵𝐶.

Q8:

A triangle has vertices at the points 𝐴, 𝐵, and 𝐶 with coordinates (2,2), (4,2), and (0,2) respectively.

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

Work out the area of the triangle 𝐴𝐵𝐶.

Q9:

Find the area of the following right-angled triangle.

Q10:

Given that 𝐴𝐵𝐶 is an isosceles triangle, where the coordinates of the points 𝐴, 𝐵, and 𝐶 are (8,2), (2,2), and (0,8), find the area of 𝐴𝐵𝐶.

Q11:

Given that the coordinates of the points 𝐴,𝐵, and 𝐶 are (2,1), (2,8), and (9,8), respectively, determine the area of 𝐴𝐵𝐶.

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

Q12:

A triangle is drawn in the coordinate plane with its vertices at 𝐴(2,2), 𝐵(7,2), and 𝐶(4.5,7).

Find the length of the base 𝐴𝐵.

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 𝐴𝐵𝐶 given the line drawn from the point 𝐴(2,8) is perpendicular to the straight line passing through the points 𝐵(4,7) and 𝐶(10,9). Give the answer to the nearest square unit.

  • A39 square unit
  • B22 square unit
  • C78 square unit
  • D19 square unit

Q14:

The quadrilateral 𝐴𝐵𝐶𝐷 is formed by the points 𝐴(15,7), 𝐵(13,3), 𝐶(5,3), and 𝐷(7,7). Calculate the length of 𝐵𝐶.

Q15:

The vertices of quadrilateral 𝑃𝑄𝑅𝑆 are 𝑃(2,7), 𝑄(8,7), 𝑅(8,3), and 𝑆(2,3). Find the lengths of 𝑃𝑄 and 𝑄𝑅.

  • A 𝑃 𝑄 = 6 , 𝑄 𝑅 = 1 0
  • B 𝑃 𝑄 = 7 , 𝑄 𝑅 = 5
  • C 𝑃 𝑄 = 1 2 , 𝑄 𝑅 = 2 0
  • D 𝑃 𝑄 = 1 0 , 𝑄 𝑅 = 6
  • E 𝑃 𝑄 = 5 , 𝑄 𝑅 = 7

Q16:

Find the area of the colored region.

Q17:

Given that the vertices of 𝑃𝑄𝑅 are 𝑃(4,4), 𝑄(3,1), and 𝑅(4,1), determine its perimeter, rounded to the nearest tenth, and then find its area.

  • Aperimeter =21, area =35
  • Bperimeter =24.2, area =21.51
  • Cperimeter =21, area =17.5
  • Dperimeter =20.6, area =35
  • Eperimeter =20.6, area =17.5

Q18:

Given that the coordinates of the points 𝐴,𝐵, and 𝐶 are (5,4), (5,5), and (6,5), respectively, determine the area of 𝐴𝐵𝐶.

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

Q19:

Given that 𝐴𝐵𝐶 is an isosceles triangle, where the coordinates of the points 𝐴, 𝐵, and 𝐶 are (8,5), (0,4), and (0,6), find the area of 𝐴𝐵𝐶.

Q20:

Find the area of the following right-angled triangle.

Q21:

Find the area of the following right-angled triangle.

Q22:

Triangle 𝐴𝐵𝐶 has vertices 𝐴(8,7), 𝐵(4,3), and 𝐶(0,1). Use vectors to determine the coordinates of the point of intersection of its medians.

  • A ( 2 , 4 )
  • B ( 1 1 , 1 5 )
  • C ( 4 , 1 )
  • D ( 4 , 1 1 )

Q23:

𝐴 𝐵 𝐶 is a triangle in which the coordinates of 𝐴, 𝐵, and 𝐶 are (1,0), (2,5), and (8,9) respectively. If 𝐴𝐷 is a median of the triangle, determine the equation of 𝐴𝐷.

  • A 𝑦 = 1 2 𝑥 + 1 2
  • B 𝑦 = 7 2 𝑥 7 2
  • C 𝑦 = 1 3 𝑥 1 3
  • D 𝑦 = 7 4 𝑥 7 4

Q24:

If 𝐴(5,8), 𝐵(6,8), and 𝐶(0,5) are vertices of a triangle, find the coordinates of the point of intersection of its medians.

  • A 3 , 3 2
  • B 4 , 1 9 4
  • C 1 1 3 , 1 1 3
  • D 1 0 3 , 1 1 3

Q25:

𝐴 𝐵 𝐶 is a right-angled triangle at 𝐵, and 𝐵𝐷 is its median from 𝐵. Given 𝐴(4,2) and 𝐶(0,1), find the coordinates of 𝐷 and the length of the median.

  • A 2 , 1 2 , 1 7 2
  • B 2 , 1 2 , 5 2
  • C ( 4 , 1 ) , 5 2
  • D 2 , 3 2 , 5

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