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?

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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?

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Answer 1 · 2018-03-20T22:45:03

Side CD = 9 units

Explanation:

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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:

$| 0 - 9 | = 9$ $| 0 - 9 | = 9$

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:

$P_{1} (9, - 9)$ $P_"1"(9, -9)$ and $P_{2} (0, - 9)$ $P_"2"(0, -9)$

In the following equation, $P_{1}$ $P_"1"$ is C and $P_{2}$ $P_"2"$ is D:

$\sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$ $sqrt((x_"2"-x_"1")^2+(y_"2"-y_"1")^2$
$\sqrt{{(0 - 9)}^{2} + (- 9 - (- 9))}$ $sqrt((0 - 9)^2 + (-9 - (-9))$
$\sqrt{{(- 9)}^{2} + {(- 9 + 9)}^{2}}$ $sqrt((-9)^2 + (-9 + 9)^2$
$\sqrt{(81) + (0)}$ $sqrt((81) + (0)$
$\sqrt{81} = 9$ $sqrt(81)=9$

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.

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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?

1 Answer

Explanation:

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