Answer:
Defining the error.
The error on this solution is that, when calculating the height, it was not calculated as an straight line. In fact, the distance that was calculated through the distance formula is the length of the side that goes from point B(5, 1) to point A (4, 3) and that's not how the height is supposed to be calculated. A correct calculation of the height should use the formula of distance and calculate the distance from the highest point of the triangle (A) to the bottom of the triangle in a straight line. Check the attached image.
Correction.
1. Calculate the base.
[tex]b=|5-1|=4[/tex]
2. Calculate the height.
Height goes from point (4, 1) and A(4, 3)
[tex]h=\sqrt{(4-4)^2+(3-1)^2} =\sqrt{4}=2[/tex]
3. Calculate area.
[tex]A=\frac{b*h}{2}=\frac{(4)(2)}{2}=\frac{8}{2} =4[/tex]
4. Express your result.
Area= 4 (units²).
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