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)

Answer 1

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

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)\| = √(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)\| = √(137)`