Worksheet Chapter 7: Coordinate Geometry

1. Given the vertices of triangle ABC are A(-2, 1), B(4, -3), and C(2, 5). (a) Calculate the area of triangle ABC. (b) State whether points A, B, and C are collinear.

2. Fill in the blank: If two non-vertical lines with gradients m₁ and m₂ are perpendicular to each other, the product of their gradients is equal to __________.

3. Line L₁ passes through points A(1, 5) and B(5, 13). (a) Find the gradient of line L₁. (b) Find the equation of line L₂ which is the perpendicular bisector of segment AB.

4. Point P(x, y) moves such that its distance from point A(0, 2) is half its distance from point B(6, 0). (a) Show that the equation of the locus of P is 3x² + 3y² + 12x - 16y - 20 = 0. (b) Find the center and radius of this circular locus.

5. A moving point P(x, y) stays at a constant distance of 4 units from point C(3, -1). (a) Find the equation of the locus of P. (b) Determine whether point Q(3, 3) lies on this locus.

6. True or False: The locus of a point P(x, y) that moves such that it is always equidistant from two fixed points A and B is the perpendicular bisector of line segment AB.

7. True or False: Three points A, B, and C are collinear if and only if the area of triangle ABC calculated using the shoelace formula is equal to zero.

8. The coordinates of three vertices of parallelogram ABCD are A(1, 2), B(5, 4), and C(7, 10). (a) Find the coordinates of vertex D. (b) Find the area of parallelogram ABCD.

9. Fill in the blank: The point that divides a line segment joining A(x₁, y₁) and B(x₂, y₂) internally in the ratio 1 : 1 is called the __________.

10. Point P divides the line segment joining A(-2, 3) and B(8, 13) internally in the ratio 3 : 2. (a) Calculate the coordinates of point P. (b) Find the distance between P and the origin (0, 0).