Homework

Coordinate Geometry

1. Find the equation of the line passing through the point (2, 5) with gradient –2. Hence, find the coordinates of the point where this line cuts the y-axis.

2. The line 3y = kx + 9 passes through a point A on the y-axis, where k is a constant.

(a) State the coordinates of A.

(b) Find the coordinates of the point where the line cuts the x-axis when k = 2.

(c) If the line passes through the point (6, 7), find the value of k.

3. The diagram shows a quadrilateral PQRS. It is given that the equation of PQ is7y – 5x = 35, and the coordinates of R and S are (h, 0) and (0, k) respectively.

(a) Find the coordinates of P and of Q.

(b) Given that the length of QR is √61 units, find the value of h.

(c) The gradient of PS is –1 1/7. Find the value of k.

(d) Using the values of h and k found in (b) and (c), find the equation of RS.

(e) The point T on the plane is such that TQ is parallel to the x-axis and TR is parallel to the y-axis. State the coordinates of T.

(f) Find the equation of TP and state the point where TP intersects the y-axis.

(g) Find the area of the quadrilateral PQRS.

4. If two lines ax + 3y – 5 = 0 and 2x – by = 4 have the same gradient, obtain an equation connecting a and b. State one possible pair of values of a and b.

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5. Find the equation of the line joining the points (2, 3) and (–4, 1). If this line intersects the line 3x – 4y + 11 = 0 at a point P, find the coordinates of P.

6. The diagram shows the graph y = h + kx – x2.Given that the curve cuts the x-axis at (3, 0) and the y-axis at (0, 3), find the

(a) value of h and of k, and

(b) equation of the line of symmetry.

7. In the diagram, AB has the same gradient as CDE. Given that the equation of CE is2y = 3x + 18, and the coordinates of A, B and E are (1, 0), (4, h) and (–8, k) respectively, find the(a) value of h and of k,

(b) coordinates of C and of D,

(c) equation of AE, and

(d) area of ΔACE.

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8. The points A(–5, 5), B(1, –3) and C(4, –3) are shown in the diagram. Find the

(a) gradient of AC,

(b) length of AB,

(c) area of ΔABC, and

(d) coordinates of the point D such that ABCD is a parallelogram.

9. The diagram shows the points A(–3, 5), B(1, –8) and C(9, 8). K is a point on BC such that AK is parallel to the x-axis.

(a) Find the equation of BC.

(b) Find the coordinates of K.

(c) Calculate the area of ΔABC.

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10. The line AB is parallel to the y-axis and the gradient of OA is the same as the gradient of CB. Given that the equation of BC is 3y = 4x + 24 and A is the point (6, k), find the

(a) value of k,

(b) coordinates of B,

(c) coordinates of P,

(d) value of h if C is the point (h, –4), and

(e) equation of AP.

End of Homework

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