Question

Cafe 103 is equidistant and colinear from metric school and angles lab. The metric school is located at (4,6) on a coordinate plane, and cafe 103 is at point (7,2). Find the coordinate of angles lab.

Answer 1

A point is aquidistance from two other points when the distance of the point from each of the other two points are equal.

Two or more points are said to be colinear when the points lie on the same line.

Given that Cafe 103 is equidistant and colinear from metric school and angles lab, this means that Cafe 103 is located at the midpoint of the line joining the points representing the metric school and angles lab.

Let the coordinates of angles lab be (x, y), then
$(7, \ 2)=\left( \frac{x+4}{2}, \ \frac{y+6}{2} \right) \\ \\ \Rightarrow x+4=2(7) \ and \ y+6=2(2) \\ \\ \Rightarrow x+4=14 \ and \ y+6=4 \\ \\ \Rightarrow x=14-4 \ and \ y=4-6 \\ \\ \Rightarrow x=10 \ and \ y = -2$

Therefore, the coordinate of angles lab is (10, -2)