Grades 7-8 Video Solutions 2023-2023_7-8

Video Transcription

Question 15. The edges of a square are one centimeter long.  How many points on the plane are exactly one centimeter away from two of the vertices of this square?  Start off by drawing our square. Since the edges of the square are one centimeter long, each one point is away from two of the vertices, so that'll be four starting off.  Next, we can draw out a blue line like so, that is one centimeter away, and  another one like so. So this will be another valid point that we can count, and  we can do this three more times for each two points.  Now we can also do the opposite of this, like so. We count the number of points that we have created, we'll get our answer, which will be E, 12.

Video Summary

The problem involves finding points on a plane that are exactly one centimeter away from two vertices of a square with one-centimeter-long edges. Initially, four points exist at the vertices. By drawing lines that are one centimeter away from pairs of vertices, additional points can be identified. Repeating this process for each pair of vertices and considering reverse scenarios results in extra points. The final count of such points, including vertices and additional derived points, equals 12, which is the solution to the problem.

Keywords

geometry

square

vertices

points

solution