Question

Jk has endpoints J(-1, 10) and K(-5, 2). MN had the endpoints M(9, -7) and N(1, -3). is JK congruent to MN?

Answer 1

Answer:

It's true that  $JK \cong MN$

Step-by-step explanation:

If the lengths of two line segments are equal, then they are said to be congruent to each other.

$JK$ has endpoints as $J(-1, 10)$, $K(-5,2)$ and $MN$ has endpoints as $M(9,-7), N(1,-3)$

Formula for finding the length of line segment: $\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2}$ , where $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ are two endpoints.

So, the length of $JK = \sqrt{(-1-(-5))^2+(10-2)^2}= \sqrt{(4)^2+(8)^2}= \sqrt{16+64}= \sqrt{80}$

and the length of $MN=\sqrt{(9-1)^2+(-7-(-3))^2}= \sqrt{(8)^2+(-4)^2}= \sqrt{64+16}= \sqrt{80}$

As, the lengths of $JK$ and $MN$ are equal, so we can say that, $JK$ is congruent to $MN$.