The rule as a mapping for the translation of a rectangle is (x, y) → (x – 2, y + 7). which describes this translation?

Translation of 2 units to the left and 7 units up.

Step-by-step explanation:

The general rule of translation is

             .... (1)

If a>0, then figure translate a units right and if a<0, then figure translate a units left.

If b>0, then figure translate b units up and if b<0, then figure translate b units down

The given rule of translation is

            .... (2)

On comparing (1) and (2), we get

a = -2 < 0, so figure translate 2 units left.

b = 7 > 0, so figure translate 7 units up.

Therefore, the given rule describes the translation of 2 units to the left and 7 units up.

the last choice

step-by-step explanation:

- "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."