Answer:
The coordinates of C and D are (1, 3) and (-5, 1), respectivelly.
Step-by-step explanation:
Since E is the midpoint of diagonals AD and BC (see attachment). That is:
[tex]AD = 2 \cdot AE[/tex]
[tex]BC = 2\cdot BE[/tex]
The vectorial distances of AE and BE are, respectively:
[tex]\overrightarrow{AE} = \vec E - \vec A[/tex]
[tex]\overrightarrow {AE} = (-2,4) -(1,7)[/tex]
[tex]\overrightarrow{AE} = (-2-1, 4-7)[/tex]
[tex]\overrightarrow {AE} = (-3,-3)[/tex]
[tex]\overrightarrow{BE} = \vec E - \vec B[/tex]
[tex]\overrightarrow {BE} = (-2,4) - (-3,5)[/tex]
[tex]\overrightarrow {BE} = (-2+3, 4-5)[/tex]
[tex]\overrightarrow {BE} = (1,-1)[/tex]
Now, the relative vectorial distances to C and D are now obtained:
[tex]\overrightarrow {AD} = 2\cdot \overrightarrow {AE}[/tex]
[tex]\overrightarrow {AD} = 2 \cdot (-3,-3)[/tex]
[tex]\overrightarrow{AD} = (-6, -6)[/tex]
[tex]\overrightarrow {BC} = 2 \cdot \overrightarrow {BE}[/tex]
[tex]\overrightarrow{BC} = 2 \cdot (1,-1)[/tex]
[tex]\overrightarrow {BC} = (2,-2)[/tex]
Lastly, the coordinates are found by the following vectorial equations:
[tex]\vec C = \vec B + \overrightarrow {BC}[/tex]
[tex]\vec C = (-3,5) + (2,-2)[/tex]
[tex]\vec C = (-3+2, 5 -2)[/tex]
[tex]\vec C = (-1,3)[/tex]
[tex]\vec D = \vec A + \overrightarrow {AD}[/tex]
[tex]\vec D = (1,7) + (-6,-6)[/tex]
[tex]\vec D = (1-6, 7 -6)[/tex]
[tex]\vec D = (-5, 1)[/tex]
The coordinates of C and D are (1, 3) and (-5, 1), respectivelly.
