Question

study the image below. find the distance between the points c(3,4) and d(4, - 2) on the coordinate plane.

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, for points $C(3,4)$ and $D(4, - 2)$, $x_1 = 3,y_1=4,x_2 = 4,y_2=-2$.

Step2: Calculate $(x_2 - x_1)$ and $(y_2 - y_1)$

$x_2 - x_1=4 - 3=1$ and $y_2 - y_1=-2 - 4=-6$.

Step3: Square the results

$(x_2 - x_1)^2=1^2 = 1$ and $(y_2 - y_1)^2=(-6)^2 = 36$.

Step4: Sum the squared results

$(x_2 - x_1)^2+(y_2 - y_1)^2=1 + 36=37$.

Step5: Calculate the distance

$d=\sqrt{37}$.

Answer:

$\sqrt{37}$