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In this lesson, we will learn how to find the side lengths, perimeter, and area of a triangle on the coordinate plane using the Pythagorean theorem.

Q1:

A triangle has vertices at the points π΄ , π΅ , and πΆ with coordinates ( 3 , 3 ) , ( β 1 , 3 ) , and ( 7 , β 6 ) respectively. Work out the perimeter of the triangle π΄ π΅ πΆ . Give your solution to two decimal places.

Q2:

A triangle has vertices at the points π΄ , π΅ , and πΆ with coordinates ( β 2 , β 2 ) , ( β 1 , 7 ) , and ( 3 , 1 ) respectively. Work out the perimeter of the triangle π΄ π΅ πΆ . 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 .

Q4:

A triangle has vertices at the points π΄ , π΅ , and πΆ with coordinates ( 0 , β 1 ) , ( 0 , 2 ) , and ( 5 , 0 ) respectively. Work out the area of the triangle π΄ π΅ πΆ .

Q5:

A triangle has vertices at the points π΄ , π΅ , and πΆ with coordinates ( 2 , β 1 ) , ( 3 , 3 ) , and ( 6 , 1 ) respectively.

Work out the perimeter of the triangle π΄ π΅ πΆ . 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 π΄ π΅ πΆ .

Q6:

Given that the vertices of β³ π π π are π ( 0 , 3 ) , π ( β 1 , β 4 ) , and π ( 3 , β 4 ) , determine its perimeter, rounded to the nearest tenth, and then find its area.

Q7:

A triangle has vertices at the points π΄ , π΅ , and πΆ with coordinates ( 0 , 5 ) , ( 1 , β 2 ) , and ( β 2 , β 2 ) respectively.

Work out the perimeter of the triangle π΄ π΅ πΆ . Give your solution to two decimal places.

Work out the area of the triangle π΄ π΅ πΆ .

Q8:

A triangle has vertices at the points π΄ , π΅ , and πΆ with coordinates ( 2 , β 2 ) , ( 4 , β 2 ) , and ( 0 , 2 ) respectively.

Q9:

Find the area of the following right-angled triangle.

Q10:

Given that π΄ π΅ πΆ is an isosceles triangle, where the coordinates of the points π΄ , π΅ , and πΆ are ( 8 , β 2 ) , ( β 2 , β 2 ) , and ( 0 , β 8 ) , find the area of β³ π΄ π΅ πΆ .

Q11:

Given that the coordinates of the points π΄ , π΅ , and πΆ are ( β 2 , 1 ) , ( β 2 , β 8 ) , and ( 9 , β 8 ) , respectively, determine the area of β³ π΄ π΅ πΆ .

Q12:

A triangle is drawn in the coordinate plane with its vertices at π΄ ( 2 , 2 ) , π΅ ( 7 , 2 ) , and πΆ ( 4 . 5 , 7 ) .

Find the length of the base π΄ π΅ .

Find the height of the triangle.

Hence, find the area of the triangle.

Q13:

Find the area of the triangle π΄ π΅ πΆ given the line drawn from the point π΄ ( β 2 , 8 ) is perpendicular to the straight line passing through the points π΅ ( 4 , β 7 ) and πΆ ( 1 0 , β 9 ) . Give the answer to the nearest square unit.

Q14:

The quadrilateral π΄ π΅ πΆ π· is formed by the points π΄ ( 1 5 , 7 ) , π΅ ( 1 3 , 3 ) , πΆ ( 5 , 3 ) , and π· ( 7 , 7 ) . Calculate the length of π΅ πΆ .

Q15:

The vertices of quadrilateral π π π π are π ( 2 , 7 ) , π ( 8 , 7 ) , π ( 8 , β 3 ) , and π ( 2 , β 3 ) . Find the lengths of π π and π π .

Q16:

Find the area of the coloured region.

Q17:

Given that the vertices of β³ π π π are π ( β 2 , 7 ) , π ( β 6 , 4 ) , and π ( 3 , 4 ) , determine its perimeter, rounded to the nearest tenth, and then find its area.

Q18:

Given that the coordinates of the points π΄ , π΅ , and πΆ are ( β 5 , 4 ) , ( β 5 , β 5 ) , and ( 6 , β 5 ) , respectively, determine the area of β³ π΄ π΅ πΆ .

Q19:

Given that π΄ π΅ πΆ is an isosceles triangle, where the coordinates of the points π΄ , π΅ , and πΆ are ( 8 , 5 ) , ( 0 , 4 ) , and ( 0 , 6 ) , find the area of β³ π΄ π΅ πΆ .

Q20:

Q21:

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