ABCD is a rectangle. Find x and y using the following information:
AB = -2x
DC = 7y + 1
AD = -x
BC = 2y + 2
To find the values of x and y in the rectangle ABCD, we can use the given information about the sides of the rectangle.
We know that opposite sides of a rectangle are equal in length, so we can set up equations using this information.
Considering AB and CD, we have:
AB = CD
-2x = 7y + 1
Similarly, considering AD and BC, we have:
AD = BC
-x = 2y + 2
Now, we have a system of two equations:
-2x = 7y + 1 ...(1)
-x = 2y + 2 ...(2)
We can solve this system of equations to find the values of x and y.
To do that, we can use the method of substitution:
From equation (2), we can solve for x:
x = -2y - 2
Now, substitute this value of x in equation (1):
-2(-2y - 2) = 7y + 1
Simplifying the equation:
4y + 4 = 7y + 1
4y - 7y = 1 - 4
-3y = -3
y = 1
Substitute the value of y = 1 back into equation (2) to find x:
x = -2y - 2
x = -2(1) - 2
x = -4
Therefore, the values of x and y in the rectangle ABCD are:
x = -4
y = 1