Question

Three vertices of a rectangle are given. Find the coordinates of the fourth vertex.

(–3, –3), (7, –3), (7, 2)

A.
(2, –3)

B.
(3, 2)

C.
(3, –2)

D.
(–3, 2)

will give medal

Answer 1

Do you know how to find the slope of a line connecting two points?

Answer 2

@Ammaar1709

Answer 3

A rectangle has two pairs of parallel lines, and two lines are parallel if they have the same slope.

Answer 4

Calculate the slopes of the lines connecting the points already given--you would have three lines from the three points.

Answer 5

And then, see which option gives the same slope as one of the slopes when connected to one of the points

Answer 6

Start with two vertex points from one side of the rectangle:
(4, 0) and (2, -3).
Subtract the X coordinates: 4 - 2 = 2
Subtract the Y coordinates: 0 - -3 = 3
Now, start with the third vertex point that is given:
(-2,4).
The differences for the X & Y coordinates between the third vertex point and the fourth vertex point will be the same as the differences between the 1st and 2nd points, so start with the 3rd point X coordinate and subtract 2 from it to get the X coordinate for the fourth point:
-2 - 2 = -4.
Then, take the 3rd point Y coordinate and subtract 4 to get the Y coordinate for the fourth point:
4 - 3 = 1
So, your fourth vertex point is (-4, 1).
See the attached picture.
This works because each of the two sets of sides of a rectangle are parallel to each other.

Answer 7

Or, you can just plot all the points out and see which looks to you as the other point of the rectangle XD