Answer:
Step-by-step explanation:
Note that in this diagram, point A represents point X, point B represents point Y, and point C represents point Z.
From the diagram, it appears as if [tex]\overline{XZ} \perp \overline{XY}[/tex]. To determine if this is the case, we can find the slopes of both segments.
[tex]m_{\overline{XZ}}=\frac{4-1}{4-1}=1\\m_{\overline{XY}}=\frac{-1-1}{3-1}=-1[/tex]
Since these slopes are negative reciprocals, we know that they are perpendicular.
This means we can use the formula [tex]A=\frac{1}{2}bh[/tex], where b is the base (XY) and h is the height (XZ).
- Note these are interchangeable.
Using the distance formula,
[tex]XY=\sqrt{(3-1)^{2}+(-1-1)^{2}}=2\sqrt{2}\\XZ=\sqrt{(4-1)^{2}+(4-1)^{2}}=3\sqrt{2}[/tex]
This means the area is [tex]\frac{1}{2}(2\sqrt{2})(3\sqrt{2})=\boxed{6}[/tex]
