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In this lesson, we will learn how to use the distance, slope, and midpoint formulas to determine the coordinates, area, and perimeter of a rectangle in the coordinate plane.
Q1:
A rectangle has vertices at the points π΄ , π΅ , πΆ , and π· with coordinates ( 1 , 1 ) , ( 4 , 2 ) , ( 6 , β 4 ) , and ( 3 , β 5 ) respectively.
Work out the perimeter of the rectangle π΄ π΅ πΆ π· . Give your solution to two decimal places.
Work out the area of the rectangle π΄ π΅ πΆ π· .
Q2:
Rectangle π΄ π΅ πΆ π· is graphed in the coordinate plane with its vertices at π΄ ( 0 , 0 ) , π΅ ( β 7 , 0 ) , πΆ ( β 7 , β 4 ) , and π· ( 0 , β 4 ) . Find its perimeter.
Q3:
Rectangle π΄ π΅ πΆ π· is graphed in the coordinate plane with its vertices at π΄ ( 0 , 0 ) , π΅ ( 6 , 0 ) , πΆ ( 6 , 5 ) , and π· ( 0 , 5 ) . Find its area.
Q4:
Rectangle π΄ π΅ πΆ π· is graphed in the coordinate plane with its vertices at π΄ ( β 3 , 4 ) , π΅ ( 5 , 4 ) , πΆ ( 5 , β 2 ) , and π· ( β 3 , β 2 ) . Find its area.
Q5:
Rectangle π΄ π΅ πΆ π· is graphed in the coordinate plane with vertices π΄ ( β 5 , β 2 ) π΅ ( 6 , β 2 ) , , and πΆ ( 6 , 3 ) . Find the coordinates of point π· .
Q6:
Given that the points π΄ ( 3 , β 6 ) , π΅ ( 1 , 2 ) , πΆ ( β 3 , β π₯ ) , and π· ( π₯ , π¦ ) are the vertices of the rectangle π΄ π΅ πΆ π· , determine the values of π₯ and π¦ .
Q7:
A parallelogram has vertices at the coordinates π΄ ( 1 , β 3 ) , π΅ ( 2 , β 1 ) , πΆ ( 5 , β 3 ) , and π· ( 4 , β 5 ) .
Work out the length of the diagonal π΄ πΆ .
Work out the length of the diagonal π΅ π· .
Using these lengths, is the parallelogram π΄ π΅ πΆ π· a rectangle?
Q8:
Given that the points π΄ ( β 5 , β 3 ) , π΅ ( β 4 , β 1 ) , and πΆ ( 0 , β 3 ) are the vertices of a right-angled triangle at π΅ , find the coordinates of the point π· that make π΄ π΅ πΆ π· a rectangle.
Q9:
The coordinates of π΄ , π΅ , and πΆ are ( 8 , β 7 ) , ( 4 , β 7 ) , and ( 4 , β 6 ) respectively. Determine the coordinates of π· that would make π΄ π΅ πΆ π· a rectangle.
Q10:
Nabil has a rectangle-shaped garden which he wants to fence. He sketched his garden on a coordinate plane with vertices at , (4,3), , and
What are the dimensions of his garden?
If each unit of the grid represents 1 m, how many meters of fencing should he buy?
Q11:
Select the expression that is equal to the area of the rectangle.
Q12:
Amira drew plans for her living room. She connected the following points, on grid paper, in order: ( 1 , 1 ) , ( 1 , 6 ) , ( 5 , 6 ) , ( 5 , 2 ) , ( 6 , 2 ) , ( 6 , 1 ) , and ( 1 , 1 ) . If the side length of each grid square represents 3 feet of the room, and Amira wants to carpet the room, how many square feet will she need to carpet?
Q13:
Given that π΄ π΅ πΆ π is a rectangle, find the length of π΄ πΆ and the area of the rectangle.
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