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:
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Here (x1,y1) are the coordinates of first point and (x2,y2) are coordinates of second point.
Putting the given values in the formula
[tex]d(P,Q) = \sqrt{(26-21)^2+(27-24)^2}\\= \sqrt{(5)^2+(3)^2}\\=\sqrt{25+9}\\=\sqrt{34}[/tex]
[tex]= 5.830952[/tex]
Rounding off: 5.83 units
The mid-point of two points is given by the formula:
[tex]M = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})[/tex]
Putting the values:
[tex]M = (\frac{21+26}{2} , \frac{24+27}{2})\\=(\frac{47}{2} , \frac{51}{2})\\=(23.5, 25.5)[/tex]
Hence,
d(P,Q) = 5.83 units
Mid-point = (23.5,25.5)
