Question

Question number 12 of 20 - geometry the coordinate values of the vertices of △klm▵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▵klm? f {(-1, 1), (-1, 4), (2, 1)} g {(0, 0), (3, 4), (0, 5)} h {(-1, 1), (-4, 5), (-1, 5)} j {(0, 0), (-5, 0), (0, 4)} questions regarding this site should be directed to steve gagnon. please include this question's id number (#7385) in your correspondence. answers

Answer 1

Two triangles are congruent if and only if they have exactly the same three sides and exactly the same three angles.

So, given that the problem establishes three vertices, we can calculate each side by this formula of distance:

$d=\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}$

We know the points:

$P_{1}(1, 1)$
$P_{1}(5, 4)$
$P_{1}(5, 1)$

Therefore:

$d_{1}=\sqrt{(1-5)^{2}+(1-4)^{2}}=5$
$d_{2}=\sqrt{(1-5)^{2}+(1-1)^{2}}=4$
$d_{3}=\sqrt{(5-5)^{2}+(4-1)^{2}}=3$

Let's take the set h and calculate the distances of each side:

$d_{1}=\sqrt{[1-(-4)]^{2}+[1-5]^{2}}=5$
$d_{2}=\sqrt{[1-(-1)]^{2}+[1-5]^{2}}=4$
$d_{3}=\sqrt{[-4-(-1)]^{2}+[5-5]^{2}}=3$

So, this set accomplish the requirement. The triangle that results from these point is congruent with Δklm