Question

Plot the following co-ordinates and find the fourth point D to make a square A (-1,3) B (1,-1) C(5,1).

Once you have found the missing coordinate use pythagoras to calculate the length of the sides.

Answer 1

1) The fourth point 'D' to make a square is D(3, 5)

2) The length of the side of the square is 2·√5 units

Explanation:

1) The coordinates to be plotted are;

A(-1, 3), B(1, -1), C(5, 1)

Using Microsoft Word, the given points are plotted and the point D is found by noting that the sides BC and AD of the square are parallel and equal in length and the point 'C' is 4 units to the right and 2 units upwards, from the point 'B', therefore, the point 'D' will be located at 4 units to the right and 2 units upwards, from the point 'A' which has coordinates of D(3, 5)

The fourth point 'D' to make a square is D(3, 5)

2) Using Pythagoras's theorem, the length of a side of the square (AB) is given as follows;

AB = √((3 - (-1))² + (1 - (-1))²) = √20 = 2·√5

The length of the side of the square, AB = BC = CD = AD = 2·√5