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 \(-\dfrac{5}{8}\).
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