Question

PLEASE HELP 8th GRADE MATH QUESTION OVER HERE!!!

Answer 1

The side AB measures option 2. $\sqrt{20}}$ units long.

Step-by-step explanation:

Step 1:

The coordinates of the given triangle ABC are A (4, 5), B (2, 1), and C (4, 1).

The sides of the triangle are AB, BC, and CA. We need to determine the length of AB.

To calculate the distance between two points, we use the formula $d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}.$

where ($x_{1},y_{1}$) are the coordinates of the first point and ($x_{2},y_{2}$) are the coordinates of the second point.

Step 2:

For A (4, 5) and B (2, 1), ($x_{1},y_{1}$) = (4, 5) and ($x_{2},y_{2}$) = (2, 1). Substituting these values in the distance formula, we get

$d=\sqrt{\left(2-4\right)^{2}+\left(1-5}\right)^{2}} = \sqrt{\left(2\right)^{2}+\left(4}\right)^{2}}=\sqrt{20}}.$

So the side AB measures $\sqrt{20}}$ units long which is the second option.