Let A=(6,2), and let B be the reflection of A over the line y = (1/2)x + 5. Find the coordinates of B
Pls help, thanks
+310 Let's start off by finding the equation of the line perpendicular to \(y=\frac{1}{2}x+5\). To do this, we note that the slope of two perpendicular lines is the negative reciprocal of each other. So we have \(y=-2x+b\). Now we plug in the point (6,2) to find that b=14. Our perpendicular line is \(y=-2x+14\).
Next, we find the intersection point of the two lines by solving for the two equations. We get the point \((\frac{18}{5}, \frac{34}{5})\).
Now, we can use the Mid-Point Formula to find our desired point, since \((\frac{18}{5}, \frac{34}{5})\) must be the midpoint of our desired point (a, b) and (6,2).
\(\frac{a+6}{2}=\frac{18}{5}\) and \(\frac{b+2}{2}=\frac{34}{5}\).
Solve for these two equations and you have your point (a, b)!
