On the coordinate plane, the segment from J(0,–7) to K(–15,–7) forms one side of a rectangle. The rectangle has a perimeter of 54 units. Select all of the points that could be a vertex of the rectangle.(–15,12)(0,–1)(0,–19)(–15,5)Submit
Question
On the coordinate plane, the segment from J(0,–7) to K(–15,–7) forms one side of a rectangle. The rectangle has a perimeter of 54 units. Select all of the points that could be a vertex of the rectangle.(–15,12)(0,–1)(0,–19)(–15,5)Submit
Solution
First, let's find the length of the segment JK. Since J and K have the same y-coordinate, the length of JK is simply the difference in their x-coordinates, which is |0 - (-15)| = 15 units.
The perimeter of a rectangle is given by the formula 2(length + width). We know the length of the rectangle is 15 units and the perimeter is 54 units. So, we can set up the equation 2(15 + width) = 54 to solve for the width. Simplifying, we get 30 + 2width = 54, so 2width = 24, and the width = 12 units.
Now, we know that the rectangle extends 12 units above and below the segment JK. So, the y-coordinates of the other two vertices of the rectangle must be -7 - 12 = -19 and -7 + 12 = 5.
Therefore, the points that could be a vertex of the rectangle are (0, -19) and (-15, 5).
Similar Questions
On the coordinate plane, the segment from M(–3,12) to N(–3,5) forms one side of a rectangle. The rectangle has a perimeter of 34 units. Select all of the points that could be a vertex of the rectangle.
On the coordinate plane, the segment from Q(6,–5) to R(–4,–5) forms one side of a rectangle. The rectangle has an area of 140 square units. Select all of the points that could be a vertex of the rectangle.
Two rectangles are shown below. Rectangle P has a perimeter of 20 inches. Rectangle Q has a perimeter of 30 inches. What are the values of j and h? Write your answer as a coordinate point with no spaces and j comes first. Example: (j,h)*1 point
Calculate the perimeter of the rectangle that has endpoints at the ordered pairs 𝐴=(3,7), 𝐵=(12,7), 𝐶=(12,4), and 𝐷=(3,4).24 units18 units30 units36 units
Find the area of △IJK with vertices I(9,5), J(–10,5), and K(9,1).
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.