ABCD is a rectangle - Edexcel - GCSE Maths - Question 19 - 2017 - Paper 1

To find the gradient of line M, we use the condition AE = EB. Given that AD is a vertical line (due to the rectangle), the positions of A and D can be expressed in terms of the coordinates from line L. Hence, the gradient of line M must be perpendicular to line L.

If the slope of line L is -\frac{1}{2}, then the slope (m) of line M is the negative reciprocal, which is 2.

Thus, we can express line M as:

$y - y_A = 2(x - x_A)$

Which we can rearrange for a specific equation.

Substituting a specific point, say A’s coordinates into the equation gives us:

For example, if A = (0, 6) (from line L), this substitution results in:

$y - 6 = 2(x - 0)$

Thus, the equation of line M becomes:

$y = 2x + 6$

This is the equation of line M based on the conditions given.