Question

Find the distance of the point (1, 2) from the mid-point of the line segment joining the points (6, 8) and (2, 4).

Answer 1

Let D(x, y) be the midpoints of A(6, 8) and B(2, 4). Let our third given point be C(1, 2). 

By midpoint formula.

x = \(\frac{x_1+x_2}2\), y = \(\frac{y_1+y_2}2\)

For midpoint D of AB,

 x = \(\frac{6+2}2\) and y = \(\frac{8+4}2\)

∴ x =4 and y = 6 

∴D(x, y) ≡ (4, 6) 

Now to find distance between C and D, 

By distance formula,

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

For CD, 

CD = \(\sqrt{(4-1)^2+(6-2)^2}\)

= \(\sqrt{9 + 16}\)

= 5 units