Question

given the points k(-1, -3), l(-6, 3), m(3, 3), and n(8, -4), disprove that $overline{kl}congoverline{mn}$. use the keypad to enter the answers in the boxes provided. round your answers to the nearest whole number. to disprove that $overline{kl}congoverline{mn}$, we apply the distance formula. the length of kl is approximately $square$, while the length of mn is approximately $square$. since the lengths are not equal, we have disproven that $overline{kl}congoverline{mn}$.

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate length of $KL$

For points $K(-1,-3)$ and $L(-6,3)$, we have $x_1=-1,y_1 = - 3,x_2=-6,y_2 = 3$.
$KL=\sqrt{(-6+1)^2+(3 + 3)^2}=\sqrt{(-5)^2+6^2}=\sqrt{25 + 36}=\sqrt{61}\approx 8$.

Step3: Calculate length of $MN$

For points $M(3,3)$ and $N(8,-4)$, we have $x_1 = 3,y_1=3,x_2 = 8,y_2=-4$.
$MN=\sqrt{(8 - 3)^2+(-4 - 3)^2}=\sqrt{5^2+(-7)^2}=\sqrt{25+49}=\sqrt{74}\approx 9$.

Answer:

The length of $KL$ is approximately $8$, while the length of $MN$ is approximately $9$.