# Lecture-3

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## 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 2a lies along the y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.

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## Part - 2

Question 3. Find the distance between P (x1, y1) and Q (x2, y2 ) 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.