Find the other endpoint of the line segment with the given endpoint and midpoint. endpoint: (-8,8) midpoint: (5,-3)

Take a look at the x-coordinates of the two given points: -8 and 5. If we depart from the left endpoint (-8,8) to the right in the direction of the midpoint (5,-3), we see that x increases by 13 as we approach the midpoint. The other endpoint is twice as far (26 units instead of 13 units) from the first one. Thus, the x-coordinate of the right endpoint is 5+13, or 18.

Take similar actions withe the y-coordinates. From y = 8 at the left endpoint, we end up at y = -3 at the midpoint, a decrease in y of 11. Decrease y again by 11 from the midpoint y-coordinate, -3, ending up with -14.

The right endpoint is thus (18, -14).

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer