Question 1119376: On a sheet of paper, graph a line segment from starting point S(2,5) to ending point E(-1,-3) and then perform the following:
a. What will be the new starting and ending points if you reflected this line segment through the line y = x ?
b. Find the point on this new (reflected) segment which is 3/4 of the way from the starting point to the ending point. What quadrant is this point in?
c. Explain how you arrived at your answers.
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
a. Reflecting the graph (ANY graph) in the line y=x simply switches the x and y values. So the new starting point is (5,2) and the new ending point is (-3,-1).
b. To find the point on the new line 3/4 of the way from the starting point to the ending point, compute the x and y values of the point sepearately.
From starting point to ending point, the change in x is -8 (from 5 to -3); 3/4 of -8 is -6; -6 from the starting x value of 5 is 5-6 = -1. The x coordinate of the point we are looking for is -1.
From the starting point to the ending point, the change in y is -3 (from 2 to -1); 3/4 of -3 is -9/4; -9/4 from the starting y value of 2 is 2-9/4 = 8/4-9/4 = -1/4. The y coordinate of the point is -1/4.
So the point is (-1,-1/4); that is in quadrant III.
c. The explanations are given above for each part.
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