ABCD is a rhombus - Edexcel - GCSE Maths - Question 18 - 2017 - Paper 1

Since ABCD is a rhombus, the diagonals AC and DB are perpendicular. Therefore, the product of their gradients must equal ( -1 ). Let the gradient of AC be ( m_{AC} ):

$m_{DB} \times m_{AC} = -1$ $-\frac{1}{2} \times m_{AC} = -1$

Solving for ( m_{AC} ):

$m_{AC} = 2$

With the gradient of AC known, we can use the point-slope form of the equation of a line. We have point A at (5, 11) and the gradient ( m_{AC} = 2 ):

Using the formula ( y - y_1 = m(x - x_1) ):

$y - 11 = 2(x - 5)$

Simplifying this gives:

$y - 11 = 2x - 10$

Thus, the equation of diagonal AC is:

$y = 2x + 1$