Line segment pq is shown on a coordinate grid: (see image below) the line segment is rotated 270 degrees counterclockwise about the origin to form p'q'. which statement describes p'q'?

It will be B equal in length cause by just rotating it. It will not change the length and your final image with not be parallel sooner or later they will touch if they go on

 The correct option is

(B) P'Q' is equal in length to PQ.

Step-by-step explanation:  Given that line segment PQ is shown on the co-ordinate grid. The line segment PQ  is rotated 270 degrees counterclockwise about the origin to form P'Q'.

We are to select the statement that describes P'Q'.

From the graph, we note that

the co-ordinates of point P are (-5, 3) and the co-ordinates of Q are (-1, 3).

So, the length of PQ as calculated using distance formula is given by

We know that if a point is rotated 270 degrees counterclockwise, then its co-ordinates changes as follows :

(x, y)  →  (y, -x).

So, after the rotation, the co-ordinates of P and Q becomes

P(-5, 3)  →  P'(3, 5)

Q(-1, 3)  →  Q'(3, 1).

The length of the line segment P'Q' as calculated using distance formula is

Thus, the lengths of PQ and P'Q' are equal.

Option (B) is CORRECT.

- "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."

solve systems of equations by graphing. a system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. the solution of such a system is the ordered pair that is a solution to both equations. to solve a system of linear equations graphically we graph both equations in the same coordinate system