The rough figure for the plot of the points is,
The obtained figure is parallelogram.
The formula for the area of parallelogram is,
[tex]A=b\cdot h[/tex]Here, b is base of parallelogram and h is height of parallelogram.
The dimension of base can be obtained by distance formula for two points on a cordinate plane. So obtain the distance between points (-4,2) and (3,-2) by using formula,
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]The height of parallelogram is equal to distance between base and its parallel line. So determine the vertical height between parallel side which is absolute value of change in y-coordinate.
Thus, for the area of parallelogram, base and height of parallelogram is required. Base is obtained by distance formula and height is equal to the chage in y-coordinate for the parallel side including the base.
Determine the length of base of parallelogram.
[tex]\begin{gathered} b=\sqrt[]{(-4-3)^2+(-2+2)^2} \\ =\sqrt[]{49} \\ =7 \end{gathered}[/tex]Determine the height of parallelogram.
[tex]\begin{gathered} h=|-2-2| \\ =|-4| \\ =4 \end{gathered}[/tex]Determine the area of parallelogram.
[tex]\begin{gathered} A=b\cdot h \\ =7\cdot4 \\ =28 \end{gathered}[/tex]Thus area of figure obtained by joining the points is 28 square units.
