## Part - 1

Derivation for angles between two lines using their slopes

Condition of slopes if two lines are parallel

Condition of slopes if two lines are perpendicular

EXERCISE 10.1 |

**Question 1. **Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.

**Question 2. **The base of an equilateral triangle with side 2*a* lies along the *y*-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.

## Part - 2

**Question 3. **Find the distance between P (*x*_{1}, *y*_{1}) and Q (*x*_{2}, *y*_{2} ) when :

(*i*) PQ is parallel to the *y*-axis,

(*ii*) PQ is parallel to the *x*-axis.

**Question 4. **Find a point on the *x*-axis, which is equidistant from the points (7, 6) and (3, 4).

**Question 5. **Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, – 4) and B (8, 0).

**Question 6. **Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle.

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