+0

# Coordinates

0
111
1

What is the y-coordinate of the point on the y-axis that is equidistant from points (-2, 0) and (-1, -4)?

Sep 5, 2021

#1
+13007
+1

What is the y-coordinate of the point on the y-axis that is equidistant from points P1(-2, 0) and P2(-1, -4)?

Hello Guest!

The center perpendicular on the line $$\overline{P_1P_2}$$ intersects the ordinate axis at that point.

$$m_{P_1P_2}=\frac{y_2-y_1}{x_2-x_1}=\frac{-4-0}{-1-(-2)}\\ m_{P_1P_2} =-4\\ m=-\frac{1}{m_{P_1P_2}}=-\frac{1}{-4}$$

$$m=\frac{1}{4}$$

$$P_m is(-1.5,-2)$$
$$f(x)=m(x-x_P)+y_P$$ $$=\dfrac{1}{4}(x-(-1.5))+(-2)\color{blue}=\dfrac{1}{4}x+\dfrac{3}{8}-2$$

$$f(0)=\dfrac{1}{4}\cdot 0+\dfrac{3}{8}-2=-\dfrac{5}{8}$$

The y-coordinate of the point on the y-axis

that is equidistant from points (-2, 0) and (-1, -4) is $$-\dfrac{5}{8}$$.

!

Sep 5, 2021