Line QR is located at Q(-5,-8) and R (-1,3) which pair of points would form a segment congruent to QR? (-4,9) and (7,5) (7,4)

Question

Line QR is located at Q(-5,-8) and R (-1,3) which pair of points would form a segment congruent to QR?
(-4,9) and (7,5)
(7,4) and (-3,5)
(3,-5) and (1,-6)
(-10,2) and (-1,6)

in progress 0
Audrey 2 weeks 2021-09-11T09:34:47+00:00 1 Answer 0

Answers ( )

    0
    2021-09-11T09:36:09+00:00

    Answer:

    (-4,9) and (7,5)

    Step-by-step explanation:

    The line QR belongs to the following family of line segments:

    \vec l_{QR} = (-1+5,3+8)

    \vec l_{QR} = (4,11)

    The length of the line segment is:

    \|l_{QR}\| = \sqrt{4^{2}+11^{2}}

    \|l_{QR}\| = \sqrt{137}

    A segment is congruent to that family of segments only if its family of line segments has the same length. Then:

    \vec l_{A} = (7+4,5-9)

    \vec l_{A} = (11, -4)

    \vec l_{B} = (-3-7,5-4)

    \vec l_{B} = (-10, 1)

    \vec l_{C} = (1-3,-6+5)

    \vec l_{C} = (-2,1)

    \vec l_{D} = (-1+10,6-2)

    \vec l_{D} = (9,4)

    Only the first option satisfies the condition of congruence, whose length is:

    \|l_{A}\| = \sqrt{11^{2}+(-4)^{2}}

    \|l_{A}\| = \sqrt{137}

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )