The perpendicular bisector to the line segment with endpoints (-3,6) and (9,2) the equation of the line is y=

y = 3x-5

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Explanation:

First find the slope of the line through the two given points. Use the slope formula for this. See figure 1 in the attached images. After following those steps, the slope happens to be -1/3. From here, you flip the fraction to get -3/1 and then you flip the sign to get +3/1 or just 3/1 which is equivalent to 3. This is the slope of the perpendicular line. The slope of the answer is m = 3, which we'll use later to help determine the y intercept.

Before we can find the y intercept, we need to know what point is on this perpendicular bisector. Recall that "bisect" means to "cut in half". So we need to find the point that cuts the segment from (-3,6) to (9,2) in half. In short: we need the midpoint. Refer to figure 2 (attached image below) to see how I found the midpoint. The short version is that you add up the corresponding coordinates and then divide by 2. The midpoint found is (3,4)

Using this midpoint (x,y) = (3,4), we can find the y intercept denoted b

y = mx+b

y = 3x+b .... plug in the slope m = 3

4 = 3*(3)+b ... plug in the point (x,y) = (3,4)

4 = 9 + b

4-9 = 9+b-9 .... subtract 9 from both sides

-5 = b

b = -5

So if m = 3 is the slope and b = -5 is the y intercept, then y = mx+b turns into y = 3x-5 which is the answer we want.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

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