#### Questions Discussed:

**Question 7.** Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.

**Question 8.** Find the value of x for which the points (x, – 1), (2, 1) \text{ and } (4, 5) are collinear.

**Question 9.** Without using distance formula, show that points (– 2, – 1), (4, 0), (3, 3) \text{ and } (–3, 2) are the vertices of a parallelogram.

**Question 10.** Find the angle between the x-axis and the line joining the points (3, –1) and (4,–2).

**Question 11. ** The slope of a line is double of the slope of another line. If tangent of the angle between them is { \displaystyle \frac{1}{3} }, find the slopes of the lines.

**Question 12. ** A line passes through { \displaystyle(x_1, y_1) } \text{ and } (h, k). If slope of the line is m, show that { \displaystyle k – y_1 = m (h – x_1) }.

**Question 13. ** If three points (h, 0), (a, b) \text{ and } (0, k) lie on a line, show that { \displaystyle \frac{a}{h} } + { \displaystyle \frac{b}{k} } = 1.

**Question 14. ** Consider the following population and year graph (Fig 10.10), find the slope of the line AB and using it, find what will be the population in the year 2010?