Question

A polygon has the following coordinates: A(4,2), B(-3,2), C(-3,5), D(4,5). Find the length of DA.
A.
4 units
B.
C.
2 units
3 units
D.
5 units
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Answer 1

Option C: 3 units is the length of DA

Explanation:

The coordinates of a polygon ABCD are $A(4,2), B(-3,2), C(-3,5), D(4,5)$

We need to find the length of DA

The length of DA can be determined using the distance formula,

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Let us substitute the coordinates $A(4,2)$ and $D(4,5)$ in the distance formula, we get,

$d=\sqrt{(4-4)^2+(5-2)^2}$

Subtracting the terms within the bracket, we have,

$d=\sqrt{(0)^2+(3)^2}$

Squaring the terms, we get,

$d=\sqrt{0+9}$

Adding the terms, we have,

$d=\sqrt{9}$

$d=3 \ units$

Thus, the length of DA is 3 units.

Hence, Option C is the correct answer.