Two of the vertices of a rectangle are 1,-6 and-8,-6 the rectangle has a perimeter of 26 units, what are the coordinates of the other two vertices
Note that the two points lie on the same horizontal line: y = -6
Graph that line segment, and it will be clear where the other two points lie, since width+height=13
Parywinkle
To find the coordinates of the other two vertices of the rectangle, we need to analyze the given information and use some mathematical reasoning.
Let's denote the coordinates of the two known vertices of the rectangle as A(1, -6) and B(-8, -6).
First, we need to determine the lengths of the sides of the rectangle. Since opposite sides of a rectangle are equal in length, we only need to find one side length, and then we can calculate the other side based on it.
The perimeter of a rectangle is defined as the sum of the lengths of all its sides. In this case, the perimeter is given as 26 units.
The two known sides of the rectangle are AB and AD. Let's assume that the side AB has length "a" units. Therefore, the side AD will also have length "a" units.
Since AB and AD are horizontal sides of the rectangle, the difference between their x-coordinates gives us the length of AB:
Length of AB = difference in x-coordinates = 1 - (-8) = 9 units
Since we know that AB = AD = a, we have a = 9 units.
Now, let's find the coordinates of points C and D, which are the other two vertices of the rectangle.
Point C will have the same y-coordinate as point A but a different x-coordinate. To find the x-coordinate of C, we can add the side length a (which is 9 units) to the x-coordinate of point A:
x-coordinate of C = x-coordinate of A + a = 1 + 9 = 10 units
So, point C has the coordinates (10, -6).
Point D will have the same x-coordinate as point B but a different y-coordinate. To find the y-coordinate of D, we can subtract the side length a (which is 9 units) from the y-coordinate of point B:
y-coordinate of D = y-coordinate of B - a = -6 - 9 = -15 units
So, point D has the coordinates (-8, -15).
Therefore, the coordinates of the other two vertices of the rectangle are C(10, -6) and D(-8, -15).