Question

what is the distance between the points (2, 10) and (-4, 2) in the xy - plane? distance = \sqrt{(y2 - y1)^2+(x2 - x1)^2} a 14 b 10 c 8 d 6

Explanation:

Step1: Identify the coordinates

Let $(x_1,y_1)=(2,10)$ and $(x_2,y_2)=(-4,2)$.

Step2: Substitute into distance formula

\[

$$\begin{align*} \text{Distance}&=\sqrt{(y_2 - y_1)^2+(x_2 - x_1)^2}\\ &=\sqrt{(2 - 10)^2+(-4 - 2)^2}\\ &=\sqrt{(-8)^2+(-6)^2}\\ &=\sqrt{64 + 36}\\ &=\sqrt{100}\\ & = 10 \end{align*}$$

\]

Answer:

B. 10