Answer:
(-4,9) and (7,5)
Step-by-step explanation:
The line QR belongs to the following family of line segments:
[tex]\vec l_{QR} = (-1+5,3+8)[/tex]
[tex]\vec l_{QR} = (4,11)[/tex]
The length of the line segment is:
[tex]\|l_{QR}\| = \sqrt{4^{2}+11^{2}}[/tex]
[tex]\|l_{QR}\| = \sqrt{137}[/tex]
A segment is congruent to that family of segments only if its family of line segments has the same length. Then:
[tex]\vec l_{A} = (7+4,5-9)[/tex]
[tex]\vec l_{A} = (11, -4)[/tex]
[tex]\vec l_{B} = (-3-7,5-4)[/tex]
[tex]\vec l_{B} = (-10, 1)[/tex]
[tex]\vec l_{C} = (1-3,-6+5)[/tex]
[tex]\vec l_{C} = (-2,1)[/tex]
[tex]\vec l_{D} = (-1+10,6-2)[/tex]
[tex]\vec l_{D} = (9,4)[/tex]
Only the first option satisfies the condition of congruence, whose length is:
[tex]\|l_{A}\| = \sqrt{11^{2}+(-4)^{2}}[/tex]
[tex]\|l_{A}\| = \sqrt{137}[/tex]
