Past Papers’ Solutions  Assessment & Qualification Alliance (AQA)  AS & A level  Mathematics 6360  Pure Core 1 (6360MPC1)  Year 2017  June  Q#4
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Question
The point A has coordinates (2,5) and the point B has coordinates (8,6).
a. Find and equation for the straight line AB, giving your answer in the form , where p, q and r are integers.
b. The point C has coordinates (k,k+1). Given that the angle ACB is a right angle, find the two possible values of k.
Solution
a.
We are required to find equation of a line AB.
To find the equation of the line either we need coordinates of the two points on the line (TwoPoint form of Equation of Line) or coordinates of one point on the line and slope of the line (PointSlope form of Equation of Line).
We are given coordinates of both points A(2,5) and B(8,6).
TwoPoint form of the equation of the line is;
Therefore for line AB;
b.
We are given that angle ACB is a right angle which means lines AC and BC are perpendicular.
If two lines are perpendicular (normal) to each other, then product of their slopes and is;
Therefore;
Expression for slope (gradient) of a line joining points and ;
Therefore, slopes of lines AC and BC are;
Hence;
We are given coordinates of points A(2,5), B(8,6) and C(k,k+1). Therefore;
Now we have two options.







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