The line segment AB with endpoints A (-3, 6) and B (9, 12) is dilated with a scale factor 2/3 about the origin. Find the endpoints of the dilated line segment.

O A) (2, 4), (6,8)

B) (4, -2), (6,8)

O C) (-2, 4), (6,8)

OD) (-2, 4), (8,6)

C) (-2, 4), (6,8) is the correct answer.

Step-by-step explanation:

Given that line segment AB:

A (-3, 6) and B (9, 12) is dilated with a scale  factor 2/3 about the origin.

First of all, let us calculate the distance AB using the distance formula:

Here,

Putting all the values and finding AB:

It is given that AB is dilated with a scale factor of .

So, the new coordinates are A'(-2,4) and B'(6,8).

Verifying this by calculating the distance A'B':

So, option C) (-2, 4), (6,8) is the correct answer.

b

step-by-step explanation:

b

- "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."