the three vertices of a rectangle abcd are a(2,2) b(-3,2) c(-3,5).plot these points on a graph paper and find the coordinates of D. Also find the area of the rectangle abcd
Answers
Given:
The three vertices of a rectangle abcd are a(2,2) b(-3,2) c(-3,5).
To find:
Plot these points on a graph paper and find the coordinates of D.
Also find the area of the rectangle abcd.
Solution:
Consider the attached figure for the plot these points on a graph paper
From given, we have,
a(2,2) b(-3,2) c(-3,5)
x1, y1 = 2, 2
x2, y2 = -3, 2
x3, y3 = -3, 5
We use the below formula to find the 4th coordinate,
(x4, y4) = [(x1 - x2) + x3, (y1 - y2) + y3 ]
= [(2 + 3) - 3, (2 - 2) + 5 ]
∴ (x4, y4) = (2, 5)
∴ The the coordinates of D is (2, 5)
The area of a rectangle given it's vertices is,
We need to use the distance formula to find the length of each side, so, we have,
AB = 5 units
BC = 3 units
CD = 5 units
DA = 3 units
∴ Area of the rectangle abcd is = l × b = 5 × 3 = 15 units
