### Video Transcript

Use a ruler and a compass to answer
this question. ๐ด, ๐ต, and ๐ถ are three
points. Another point, ๐, is four
centimetres away from ๐ด. It is also the same distance from
๐ต and ๐ถ. Mark one of the possible positions
of point ๐.

Now itโs important to say that, for
this question, you need to print it at 100-percent scale. Donโt 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.

Weโre 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. Thatโs 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: ๐ด, ๐ต, and ๐ถ. And we have to work out where
another point, ๐, is, which is four centimetres away from ๐ด. And weโre also told that point ๐
is the same distance away from points ๐ต and ๐ถ. Sometimes thatโs written as being
equidistant from ๐ต and ๐ถ.

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 itโs exactly four centimetres. Then with the radius set to exactly
four centimetres, we can place the compass point exactly on point ๐ด and draw a
circle, centre ๐ด, 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 ๐ต and ๐ถ, we need to put the compass point at ๐ถ,
then open up the radius to over half the distance from ๐ถ to ๐ต. Now it doesnโt matter exactly what
that radius is so long as itโs over half the distance from ๐ถ to ๐ต.

Then we carefully draw an arc. Whatever radius you used, itโs
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 ๐ต 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 ๐ต and ๐ถ, then you will
be able to create a second arc so that it cuts the first arc in two places. If we wouldโve gone for a slightly
smaller radius, our arcs wouldโve intersected slightly close together. And if weโd gone for a slightly
larger radius, theyโd intersect a little bit further apart.

Now draw a line between your points
of intersection and extend it through the circle around point ๐ด. Now when youโve done this, youโll
find that all of the points on this line are equidistant from points ๐ต and ๐ถ. In other words, any point on that
line is the same distance away from point ๐ต as it is from point ๐ถ.

And remember, we said that all of
the points on this circle are four centimetres away from ๐ด. 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 ๐ด and also on the line of points which are equidistant from
๐ต and ๐ถ. So we got two possible positions
for our point ๐.

The question asked us to mark one
of the possible positions of point ๐. 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 ๐ may be slightly
different to our position of ๐. But hopefully, going through this
video has helped you to work out what the steps are in answering this question.