Use a ruler and a compass to answer
this question. 𝐴, 𝐵, and 𝐶 are three
points. Another point, 𝑃, is four
centimetres away from 𝐴. It is also the same distance from
𝐵 and 𝐶. Mark one of the possible positions
of point 𝑃.
Now it’s important to say that, for
this question, you need to print it at 100-percent scale. Don’t use the scale-to-fit paper
option when printing out the question. If you print it out at a slightly
different size, because this is a scale drawing question involving constructions,
your answer will look a little bit different to ours.
We’re told to use a ruler and
compass to answer this question. And that makes it an accurate
construction question. That means we got to make marks on
the page and not rub them out. That’s our working out. If we rub out all of our working
out lines, then we may lose marks.
Our diagram then gives us three
points: 𝐴, 𝐵, and 𝐶. And we have to work out where
another point, 𝑃, is, which is four centimetres away from 𝐴. And we’re also told that point 𝑃
is the same distance away from points 𝐵 and 𝐶. Sometimes that’s written as being
equidistant from 𝐵 and 𝐶.
Our first task then is to get the
compasses and ruler out. Put the compass point exactly on
zero mark on the ruler. Then carefully open up the radius
until it’s exactly four centimetres. Then with the radius set to exactly
four centimetres, we can place the compass point exactly on point 𝐴 and draw a
circle, centre 𝐴, with radius four centimetres. Then check carefully with your
ruler that the radius of this circle is indeed exactly four centimetres.
Then to find the set of points
which are equidistant from points 𝐵 and 𝐶, we need to put the compass point at 𝐶,
then open up the radius to over half the distance from 𝐶 to 𝐵. Now it doesn’t matter exactly what
that radius is so long as it’s over half the distance from 𝐶 to 𝐵.
Then we carefully draw an arc. Whatever radius you used, it’s
important that you take great care to keep that radius exactly the same for the next
step. And with that same radius,
carefully put the compass point at 𝐵 and draw another arc intersecting the first
arc that you drew.
Now provided you made sure that the
radius of your compasses was over half the distance between 𝐵 and 𝐶, then you will
be able to create a second arc so that it cuts the first arc in two places. If we would’ve gone for a slightly
smaller radius, our arcs would’ve intersected slightly close together. And if we’d gone for a slightly
larger radius, they’d intersect a little bit further apart.
Now draw a line between your points
of intersection and extend it through the circle around point 𝐴. Now when you’ve done this, you’ll
find that all of the points on this line are equidistant from points 𝐵 and 𝐶. In other words, any point on that
line is the same distance away from point 𝐵 as it is from point 𝐶.
And remember, we said that all of
the points on this circle are four centimetres away from 𝐴. If you look carefully, you can see
that there are two points which are both on that circle of points which are four
centimetres away from 𝐴 and also on the line of points which are equidistant from
𝐵 and 𝐶. So we got two possible positions
for our point 𝑃.
The question asked us to mark one
of the possible positions of point 𝑃. So either one of those is a correct
answer. And finally, if your printer did
print this off at a different scale, then your position of 𝑃 may be slightly
different to our position of 𝑃. But hopefully, going through this
video has helped you to work out what the steps are in answering this question.