Three vertices of a rectangle are located on the coordinate plane shown below.
An x y coordinate grid with points A B and C. Point A is at 2 comma 8, point B is at 6 comma 8, and point C is at 6 comma 1.
What are the coordinates of the fourth vertex of the rectangle?
ever think of actually typing the coordinates?
A=(2,8) B=(6,8) C=(6,1)
Clearly, AB is a side of length 4
So, CD must also have length 4, 7 units below AB.
What do you think?
If nothing else, plot the points A,B,C and see where D must be.
To find the coordinates of the fourth vertex of the rectangle, we can use the property of rectangles that opposite sides are parallel and equal in length.
Since points A and B have the same y-coordinate, and the opposite sides of a rectangle are parallel, we can conclude that the fourth vertex must have the same y-coordinate as points A and B.
Since points B and C have the same x-coordinate, and the opposite sides of a rectangle are parallel, we can conclude that the fourth vertex must have the same x-coordinate as points B and C.
Therefore, the coordinates of the fourth vertex of the rectangle are (2, 1).
To find the coordinates of the fourth vertex of the rectangle, we need to understand the properties of rectangles. A rectangle has four right angles, and the opposite sides are parallel and equal in length.
Since we know three vertices of the rectangle, A, B, and C, we can use this information to find the fourth vertex.
Let's start by determining the length of the sides of the rectangle. We can calculate this by finding the distance between two points using the distance formula:
Distance = √[(x2 - x1)² + (y2 - y1)²]
Let's calculate the length of AB:
Length of AB = √[(6 - 2)² + (8 - 8)²]
= √[(4)² + (0)²]
= √[16 + 0]
= √16
= 4
Now, let's calculate the length of BC:
Length of BC = √[(6 - 6)² + (1 - 8)²]
= √[(0)² + (-7)²]
= √[0 + 49]
= √49
= 7
Since AB and BC are parallel sides, the length of AB is equal to the length of CD (opposite sides are equal in a rectangle), and the length of BC is equal to the length of AD.
Now, let's find the coordinates of the fourth vertex, D.
Starting from point B, we move 4 units horizontally (equal to the length of AB) and 7 units vertically (equal to the length of BC) to reach the fourth vertex, D.
Coordinates of point B: (6, 8)
Moving horizontally 4 units to the right: (6 + 4, 8) = (10, 8)
Moving vertically 7 units downward: (10, 8 - 7) = (10, 1)
Therefore, the coordinates of the fourth vertex, D, are (10, 1).