Question

For the point P(21, 24) and Q(26, 27) , find the distance d(P, Q) and the coordinates of the midpoint M of the segment PQ

Answer 1

Answer:

d(P,Q) = 5.83 units

Mid-point = (23.5,25.5)

Step-by-step explanation:

Given points are:

P(21,24) = (x1,y1)

Q(26,27) = (x2,y2)

The distance formula is given by:

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

Here (x1,y1) are the coordinates of first point and (x2,y2) are coordinates of second point.

Putting the given values in the formula

$d(P,Q) = \sqrt{(26-21)^2+(27-24)^2}\\= \sqrt{(5)^2+(3)^2}\\=\sqrt{25+9}\\=\sqrt{34}$

$= 5.830952$

Rounding off: 5.83 units

The mid-point of two points is given by the formula:

$M = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})$

Putting the values:

$M = (\frac{21+26}{2} , \frac{24+27}{2})\\=(\frac{47}{2} , \frac{51}{2})\\=(23.5, 25.5)$

Hence,

d(P,Q) = 5.83 units

Mid-point = (23.5,25.5)