Competition problem — Geometry — Maths Olympiad Prep

Library / /90 of 520

Geometry Difficulty 2.8 Junior Find the answer

The midpoint coordinates of points $A(7,8)$ and $B(1,2)$ are:

Pick one

Solution

To find the midpoint of a line segment with endpoints $A(7,8)$ and $B(1,2)$ , we use the midpoint formula, which is given by the average of the $x$ -coordinates and the $y$ -coordinates of the endpoints. Thus, the midpoint $M$ has coordinates $(x_M, y_M)$ where:

$x_M = \frac{x_A + x_B}{2} = \frac{7 + 1}{2} = \frac{8}{2} = 4$

and

$y_M = \frac{y_A + y_B}{2} = \frac{8 + 2}{2} = \frac{10}{2} = 5$

Therefore, the coordinates of the midpoint are $(4, 5)$ .

So, the correct answer is $\boxed{B}$ .

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.