For the point p(21,19) and q(28.24), find the distance d(p, q) and the coordinates of the
midpoint m of the segment pq

1. √74; 2. (24.5, 21.5)

Step-by-step explanation:

1. Distance

You could use the distance formula to calculate the length of PQ, but I prefer a visual approach, because it requires less memorization.

Draw a horizontal line from P and a vertical line from Q until they intersect at R (28, 19).

Then you have a right triangle PQR, and you can use Pythagoras' theorem to calculate PQ.

2. Midpoint of line

The coordinates of the midpoint are half-way between the x- and y-coordinates of the end points.

For the x-coordinate, the half-way point is

(21 + 28)/2 = 49/2 = 24.5

For the y-coordinate,  the half-way point is

(19 +24)/2 = 43/2 = 21.5

The coordinates of the midpoint M are (24.5, 21.5).

there is no image attacted

x^3-4x^2+3x-2/x^2+1

step-by-step explanation:

factor the numerator and denominator and cancel the common factors