Question

The coordinate values of the vertices of △klm are integers. triangle klm has vertices located at (1, 1), (5, 4) and (5, 1). which set of coordinate pairs could represent the vertices of a triangle congruent to △klm?

Answer 1

The rest of the queastion is :
A) (-1, 1), (-1, 4), (2, 1)
B) (0, 0), (3, 4), (0, 5)
C) (-1, 1), (-4, 5), (-1, 5)
D) (0, 0), (-5, 0), (0, 4)
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The distance between two points (x₁,y₁),(x₂,y₂) = d
$d = \sqrt{ (x2-x1)^{2} + (y2-y1)^{2} }$

we have K(1, 1), L(5, 4) and M(5, 1)
we will find the length between each two points.
KL = $d = \sqrt{ (5-1)^{2} + (4-1)^{2} }$ = 5
LM = $d = \sqrt{ (5-5)^{2} + (1-4)^{2} }$ = 3
KM = $d = \sqrt{ (5-1)^{2} + (1-1)^{2} }$ = 4

now check each group from the choices
the group that will give the same result will be the correct choice.
The correct choice is C
C) (-1, 1), (-4, 5), (-1, 5)

check the answer;
K'(-1, 1), L'(-4, 5), M'(-1, 5)

K'L' = $d = \sqrt{ (-4+1)^{2} + (5-1)^{2} }$ = 5
L'M' = $d = \sqrt{ (-1+4)^{2} + (5-5)^{2} }$ = 3
K'M' = $d = \sqrt{ (-1+1)^{2} + (5-1)^{2} }$ = 4