Question

The approximate length of side XY is a: 3b: 3.16c: 4d: 4.24 units.

Answer 1

Given a triangle XYZ on the graph

The coordinates of points X, Y and Z are

`\begin{gathered} X\Rightarrow(-3,-1) \\ Y\Rightarrow(-2,-4) \\ Z\Rightarrow(-6,-4) \end{gathered}`

To find the approximate length of the sides, we apply the formula to find the distance, d, between two points which is

`d=√((x_2-x_2)^2+(y_2-y_1)^2)`

To find the approximate length of side XY, substitute the coordinates of points X and Y into the formula to find the distance, d, between two points

`\begin{gathered} XY=√((-3-(-2))^2+(-4-(-1))^2) \\ XY=√((-1)^2+(-3)^2) \\ XY=√(1+9)=√(10)=3.16\text{ units} \\ XY=3.16\text{ units} \end{gathered}`

Hence, the approximate length of side XY is 3.16 units (option b)