Question

Given the rectangle ABCD as shown, find the value for x if DO = 5x -9 and CO = x + 7

x =___

Answer 1

In rectangle ABCD, let's label the corners as follows:

- A = (0, 0)
- B = (a, 0)
- C = (a, b)
- D = (0, b)

O is the point where diagonals AC and BD intersect. In a rectangle, point O is the midpoint of both diagonals AC and BD, which means that DO = OC and AO = OB.

Given:

- \( DO = 5x - 9 \)
- \( CO = x + 7 \)

Since O is the midpoint, we know that \( DO = OC \). Therefore, we can set the expressions equal to each other:

\[
5x - 9 = x + 7
\]

Now, solve for x:

1. Subtract \( x \) from both sides:

\[
5x - x - 9 = 7
\]

This simplifies to:

\[
4x - 9 = 7
\]

2. Add 9 to both sides:

\[
4x = 16
\]

3. Divide by 4:

\[
x = 4
\]

Thus, the value for \( x \) is:

\[
x = 4
\]