Points J and K, plotted on the coordinate grid, are two vertices of rectangle JKLM. Rectangle JKLM has an area of 7 square units. Point J is located at (2, 1) and point K is located at (-5,1) each vertex of the rectangle is located at a point that has integer coordinates.
Part A which points could be another vertex of the rectangle.(-5 0) (-5 2) (1,1) (2, -6) (2,0) (9,1) (2, 2)
What is the perimeter of rectangle JKLM?
16 Units
A. J(2,1), K(-5,1), L(-5,2), M(2,2).
B. L = 2 - (-5 = 7, W = 2-1 = 1.
P = 2L + 2W = 2*7 + 2*1 = 16 Units.
no way
The answer is D, A, AND B
To find the other two vertices of the rectangle, we need to determine the side lengths of the rectangle.
The length of the rectangle can be found by calculating the distance between points J and K. The formula to find the distance between two points is the square root of the sum of the squares of the differences of their coordinates.
In this case, the x-coordinates of J and K are 2 and -5 respectively, while their y-coordinates are both 1.
Using the distance formula, we can calculate the length of the rectangle as:
Length = √[(-5 - 2)^2 + (1 - 1)^2] = √[49 + 0] = √49 = 7
Similarly, the width of the rectangle can be found by calculating the distance between points K and one of the potential vertices. Let's consider each potential vertex in turn:
- Vertex (-5, 0): Width = √[(2 - (-5))^2 + (1 - 0)^2] = √[49 + 1] = √50. Not an integer length, so this is not a valid vertex.
- Vertex (-5, 2): Width = √[(2 - (-5))^2 + (1 - 2)^2] = √[49 + 1] = √50. Not an integer length, so this is not a valid vertex.
- Vertex (1, 1): Width = √[(1 - (-5))^2 + (1 - 1)^2] = √[36 + 0] = √36 = 6. Valid vertex length.
- Vertex (2, -6): Width = √[(2 - (-5))^2 + (1 - (-6))^2] = √[49 + 49] = √98. Not an integer length, so this is not a valid vertex.
- Vertex (2, 0): Width = √[(2 - (-5))^2 + (1 - 0)^2] = √[49 + 1] = √50. Not an integer length, so this is not a valid vertex.
- Vertex (9, 1): Width = √[(2 - 9))^2 + (1 - 1)^2] = √[49 + 0] = √49 = 7. Valid vertex length.
- Vertex (2, 2): Width = √[(2 - (-5))^2 + (1 - 2)^2] = √[49 + 1] = √50. Not an integer length, so this is not a valid vertex.
The valid vertices are (1, 1) and (9, 1), which means the other two vertices of the rectangle are L(1, 1) and M(9, 1).
To find the perimeter of the rectangle, we can calculate the sum of the lengths of all four sides.
Perimeter = 2 * (Length + Width) = 2 * (7 + 6) = 2 * 13 = 26 units.
Therefore, the perimeter of rectangle JKLM is 26 units.