How do this maths question?

Question

Please leave working out if you know the answer, thanks :)

Answer 1

Capt. Matticus is right in calculating the size of the grid. The side of one box is 4 mm wide.

However, he apparently misread the question. You're asked to work out the distance between M and J, not M and K.

Which makes the problem a lot easier, of course!   :-)

The line of symmetry goes through points K and L as you probably realize. So, point M is on the same horizontal line than point J, just below the letter "p" of "five points".

Since J is 3 boxes to the left from the line of symmetry, point M will therefore be 3 boxes to the right.

In total, the distance between J and M is 6 boxes, equivalent to 24 mm.

Answer 2

First, figure out the size of a grid.  There are 7 boxes between k and l and we're told that they're 28 mm apart.

28 mm / 7 boxes = 4 mm/boxes

If you drew a line between k and l, you'd hopefully see how there's a corresponding point for j that is missing.  So, just find the distance from j to k and that'll be the distance from k to m.

j and k are separated by 2 vertical spaces and 3 horizontal spaces

4 * sqrt(2^2 + 3^2) =>

4 * sqrt(4 + 9) =>

4 * sqrt(13) =>

14.42220510185595717247688506988....

14.4222 mm

14.4 mm

or 4 * 13^(1/2) mm.

See which one works.