**“To live a creative life, we must lose our fear of being wrong.”**

# Lecture - 3 Chapter 10 Straight Lines

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.

**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.