One endpoint of a line segment is (8, −1). the point (5, −2) is one-third of the way from that endpoint to the other endpoint. find the other endpoint

The other endpoint is (-4, -5)

Step-by-step explanation:

We know the formula for the coordinates of the point dividing the line segment in the ratio of a : b is

x = x' +

y = y' +

Now we plug in the values of endpoints (8, -1) and (x, y) with a point (5, -2) dividing the segment in 1 : 3 ratio.

5 = 8 +

5 - 8 =

(x - 8) = -3×4 = -12

x = -12 + 8 = -4

Similarly, -2 = -1 +

-2 + 1 =

y + 1 = -1(4)

y + 1 = -4

y = -1 - 4 = -5

Therefore, another endpoint of the segment is (-4, -5).

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."