Using geometric methods to solve design problems
About this video
A festival map is split by perpendicular bisectors into regions closest to charging stations A, B and C. The video uses the fact that every point on one side of a perpendicular bisector is closer to the endpoint on that side to work out that Zara is closest to station C.
You'll be able to
- explain why points on one side of a perpendicular bisector are closer to one endpoint.
- use perpendicular bisectors on a map to decide which location is closest to a point.
Key words
- perpendicular bisector
- A line that crosses a segment at its midpoint at a right angle; every point on it is the same distance from both endpoints.
- partitioned
- Divided up into separate regions or parts.
- equidistant
- The same distance from two or more points.
Transcript
- [Narrator] We're told the map shows a music festival partitioned by perpendicular bisectors into regions closest to phone charging stations A, B, and C. Zara is at location Z. All right, this is Zara right over here. Based on the map, which phone charging station is closest to Zara?
Pause this video. Have a go at that before we do it together. All right, now let's do it together. So first of all, we need to interpret what these lines are and to see that they're perpendicular bisectors and maybe I'll color code it. So if I were to draw the segment connecting A and C, we can see that the perpendicular bisector is this line right over there and out of all of 'em, this is the only one that looks like it intersects at a perpendicular right over there and it's halfway between A and C.
And just from that, we can see that given that Zara is to the right of that perpendicular bisector, she must be closer to C than A. So we can rule out that A is the one that Zara is closest to. So now the choice is between C and B, but once again, we can look at another perpendicular bisector.
Actually, let me do this in pink. So that's the segment that connects B and C and the perpendicular bisector is this line right over here. It bisects it. So this length is equivalent to that length. Anything above it is gonna be closer to C. Anything below is gonna be closer to B.
So this is Z, or Zara, is above and to the right, so it's on the same side as C, so it's also closer to C than it is to B. So from that, we know that Zara is closest to the phone charging station at C.
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