Question

For the point P(25,-15) and Q​(30,-12), find the distance​ d(P,Q) and the coordinates of the midpoint M of the segment PQ.

Answer 1

Answer:

$d(P,Q) = \sqrt{34}$

The midpoint of the segment is M(27.5, -13.5).

Step-by-step explanation:

Distance between two points:

Suppose that we have two points, $(x_1,y_1)$ and $(x_2,y_2)$. The distance between them is given by:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Distance between P(25,-15) and Q​(30,-12)

$d(P,Q) = \sqrt{(30-25)^2+(-12-(-15))^2} = \sqrt{34}$

So

$d(P,Q) = \sqrt{34}$

Coordinates of the midpoint M of the segment PQ.

Mean of the coordinates of P and Q. So

$x_M = \frac{25+30}{2} = \frac{55}{2} = 27.5$

$y_M = \frac{-15-12}{2} = -\frac{27}{2} = -13.5$

The midpoint of the segment is M(27.5, -13.5).