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

d(P,Q) = 5.83 units

Mid-point = (23.5,25.5)

Explanation:

Given points are:

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

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

The distance formula is given by:

`d = √((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) = √((26-21)^2+(27-24)^2)\\= √((5)^2+(3)^2)\\=√(25+9)\\=√(34)`

`= 5.830952`

Rounding off: 5.83 units

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

`M = ((x_1+x_2)/(2) , (y_1+y_2)/(2))`

Putting the values:

`M = ((21+26)/(2) , (24+27)/(2))\\=((47)/(2) , (51)/(2))\\=(23.5, 25.5)`

Hence,

d(P,Q) = 5.83 units

Mid-point = (23.5,25.5)