Question

Gregory drew a rectangle ABCD on a coordinate plane. Point A is at (0,0). Point B is at (9,0). Point C is at (9,-9). Point D is at (0,-9). Find the length of side CD?

Answer 1

Side CD = 9 units

Explanation:

If we ignore the y coordinates (the second value in each point), it's easy to tell that, since side CD starts at x = 9, and ends at x = 0, the absolute value is 9:

`| 0 - 9 | = 9`

Remember that the solutions to absolute values are always positive

If you don't understand why this is, you can also use the distance formula:

`P_"1"(9, -9)` and `P_"2"(0, -9)`

In the following equation, `P_"1"` is C and `P_"2"` is D:

`sqrt((x_"2"-x_"1")^2+(y_"2"-y_"1")^2`
`sqrt((0 - 9)^2 + (-9 - (-9))`
`sqrt((-9)^2 + (-9 + 9)^2`
`sqrt((81) + (0)`
`sqrt(81)=9`

Obviously that's the most detailed and algebraic explanation you could find, and is much more work than needed, but if you were wondering "why," that's why.