Questions covered in Standard

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. The value of $x$ for which the points $(x, -1), (2, 1)$ and $(4, 5)$ are collinear is
2. The equation of the line passing through $(1, 2)$ and perpendicular to $x + y + 7 = 0$ is
3. The distance between the parallel lines $3x - 4y + 7 = 0$ and $3x - 4y + 5 = 0$ is
4. The angle between the lines $y - \sqrt{3}x - 5 = 0$ and $\sqrt{3}y - x + 6 = 0$ is
5. The coordinates of the foot of the perpendicular from the point $(2, 3)$ on the line $x + y - 11 = 0$ are
6. Find the equation of the line passing through the point $(-4, 3)$ with slope $1/2$.
7. Find the value of $k$ for which the line $(k-3)x - (4-k^2)y + k^2 - 7k + 6 = 0$ is parallel to the x-axis.
8. Find the distance of the point $(3, -5)$ from the line $3x - 4y - 26 = 0$.
9. Find the equation of the line perpendicular to the line $x - 7y + 5 = 0$ and having x-intercept 3.
10. The vertices of a triangle are $A(2, 3), B(4, -1)$ and $C(1, 2)$. Find the length of the altitude from vertex A to the side BC.
11. Find the image of the point $(3, 8)$ with respect to the line $x + 3y = 7$ assuming the line to be a plane mirror.
12. Case Study: A line forms a triangle of area $54\sqrt{3}$ square units with the coordinate axes. The perpendicular from the origin to the line makes an angle of $60^\circ$ with the positive x-axis.
    (i) Find the equation of the line in normal form.
    (ii) Find the intercepts on the axes in terms of $p$.
    (iii) Find the value of $p$ and the equation of the line.