Numerical: coordinate geometry MCQ - Practice Questions with Answers

Put y = 0 in 2x - 3y + 6 = 0 to get x = -3, so the x-intercept has length 3. Put x = 0 to get -3y + 6 = 0, hence y = 2, so the y-intercept has length 2. The triangle with the coordinate axes is right-angled, so its area is 1/2 x 3 x 2 = 3 square units. Therefore 4, 7 and 10 square units are too large for these intercepts.

The x-axis is y = 0. The line 2x + y = 4 meets it at x = 2, so one point is (2, 0). The line x - y + 1 = 0 gives y = x + 1 and meets the x-axis at x = -1, so the second point is (-1, 0). Solving 2x + y = 4 and y = x + 1 gives x = 1 and y = 2, the third point. The base on the x-axis is 3 units and the height is 2 units, so the area is 1/2 x 3 x 2 = 3 square units.

Using the distance formula, AB, BC, CD and DA all have the same length: the squared length is 388 in each case. The adjacent sides are therefore equal, which gives a rhombus. It is not a rectangle because adjacent sides are not perpendicular; their slopes do not multiply to -1. It is not a square because a square would also require right angles. It is not merely a trapezium, since the stronger condition of all four sides being equal is satisfied.