Question

segment ab has point a located at (4, 2). if the distance from a to b is 3 units, which of the following could be used to calculate the coordinates for point b?
3 = \sqrt{(x - 2)^2+(y - 4)^2}
3 = \sqrt{(x - 4)^2+(y - 2)^2}
3 = \sqrt{(x + 2)^2+(y + 4)^2}
3 = \sqrt{(x + 4)^2+(y + 2)^2}

Explanation:

Step1: Recall distance formula

The distance $d$ 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, $A=(4,2)$ and $B=(x,y)$, and $d = 3$.

Step2: Substitute values

Substitute $x_1 = 4$, $y_1=2$, and $d = 3$ into the distance formula. We get $3=\sqrt{(x - 4)^2+(y - 2)^2}$.

Answer:

$3=\sqrt{(x - 4)^2+(y - 2)^2}$