Coordinate Geometry

Fill in all the gaps, then press "Check" to check your answers. Use the "Hint" button to get a free letter if an answer is giving you trouble. You can also click on the "[?]" button to get a clue. Note that you will lose points if you ask for hints or clues!

1. The integral values of m for which the x-coordinate of the point of intersection of the lines y = mx + 1 and 3x + 4y = 9 is an integer is - , - .
2. If the point (5, 2) bisects the intercept of a line between the axes, then its equation is x + y = 20.
3. The figure formed by the lines

a x \pm b y \pm c = 0

is a .
4. The value of

λ

for which the lines

3 x + 4 y = 5

5 x + 4 y = 4

and

λ x + 4 y = 6

meet at a point is .
5. Three vertices of a parallelogram taken in order are (- 1, - 6), (2, - 5) and (7, 2). The fourth vertex is (, ).
6. If the lines x + q = 0, y - 2 = 0 and 3x + 2y + 5 = 0 are concurrent, then the value of q will be .
7. The equation of the line with slope

\frac{- 3}{2}

and which is concurrent with the lines 4x + 3y - 7 = 0 and 8x + 5y - 1 = 0 is x + 2y - = 0.
8. The point on the x-axis which is equidistant from points (- 1, 0) and (5, 0) is (, ).
9. If points A(5, p), B(1, 5), C(2, 1) and D(6, 2) form a square. Then p = .
10. The distance of the point (4, 7) from the y-axis is units.

Coordinate Geometry

Gap-fill exercise