Find the equation of the perpendicular bisector of the line segment joining the points (1, 2) and (-2, 1)
Does it mean I have to find the line. Then find a line that cuts that line in to half because perpendicular bisector
just find the slope of the line: 1/3
the perp has slope -3, so now we have a midpoint (-1/2,3/2) and a slope (-3), and our line is
y - 3/2 = -3(x + 1/2)
So the equation is -3(x+1/2)?
Like there's no Y= in it?
I gave you the equation. There's always a y. If you want it it slope-intercept form, which most people find comforting, that would be
y = -3x
Visit
http://rechneronline.de/function-graphs/
and plot the two functions
(x+5)/3 and -3x
and you will see that the two lines intersect midway between the two given points
Yes, you are correct! To find the equation of the perpendicular bisector, you first need to find the equation of the line that passes through the midpoint of the given segment and is perpendicular to it. Here's a step-by-step guide on how to do that:
1. Find the midpoint of the line segment using the midpoint formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
For the given points (1, 2) and (-2, 1), the midpoint is ((1 + -2) / 2, (2 + 1) / 2) = (-1/2, 3/2).
2. Find the slope of the line segment using the slope formula:
Slope = (y2 - y1) / (x2 - x1)
For the given points, the slope is (1 - 2) / (-2 - 1) = -1 / -3 = 1/3.
3. The slope of the perpendicular bisector will be the negative reciprocal of the slope of the line segment. So, the slope of the perpendicular bisector is -3 (reciprocal of 1/3).
4. Now, you have the slope of the perpendicular bisector and the midpoint. Use the point-slope form of the equation of a line to find its equation:
y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Using the midpoint (-1/2, 3/2) and the slope -3, the equation becomes:
y - 3/2 = -3(x - (-1/2))
Simplifying further, we get: y - 3/2 = -3x - 3/2
Rearranging the equation, we get the equation of the perpendicular bisector:
y = -3x
Therefore, the equation of the perpendicular bisector of the line segment joining the points (1, 2) and (-2, 1) is y = -3x.