Question

Find the coordinates of the points B, C, D in the picture below:

Write the lengths AB, BC, CD in the order of their magnitudes.

Answer 1

For knowing the coordinates of points B, C and D, we need to know the length of the line segments BA, CA and DA respectively.

We know that distance between two points is given by:

D =

Now, OA =

ΔBAO is a right angled triangle, right angled at A.

Here, ∠BOA = 30°

∴ Tan 30° =

Also, ΔCAO is a right angled triangle, right angled at A.

Here, ∠COA = 30° + 15° = 45°

∴ Tan 45° =

ΔDAO is a right angled triangle, right angled at A.

Here, ∠DOA = 30° + 15° + 15° = 60°

∴ Tan 60° =

Points A, B, C and D all lie on a line parallel to y-axis.

Since, the distance between point A and y-axis is 9 units, the distance between points B, C and D and y-axis is also 9 units.

Thus, the coordinates of points B, C and D are (9, ), (9, 9) and (9, ) respectively.

Now, AB =

BC = AC − AB =

CD = AD − AC =

Thus, the lengths of AB, BC and CD in order of their magnitudes are: