The points A(1, 2), B(7, 2) and C(k, 4), where k is a constant, are the vertices

Question:

The points A(−1, −2), B(7, 2) and C(k, 4), where k is a constant, are the vertices of △ABC. Angle ABC is a right angle.

a. Find the gradient of AB.

b. Calculate the value of k.

c. Find an equation of the straight line passing through B and C. Give your answer in the form ax + by + c = 0, where a, b and c are integers

d. Calculate the area of △ABC.

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