Chapter 9
Draw a quadrilateral in the Cartesian plane, whose vertices are (- 4, 5), (0, 7), (5, - 5) and (- 4, -2). Also, find its area.
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.
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.
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
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).
Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (-1, -1) are the vertices of a right angled triangle.
Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.
Without using distance formula, show that points ( - 2, - 1), (4, 0), (3, 3) and (-3, 2) are the vertices of a parallelogram.
Find the angle between the x-axis and the line joining the points (3,-1) and (4,-2).
The slope of a line is double of the slope of another line. If tangent of the angle between them is 3 , find the slopes of the lines.
A line passes through (x1, y1) and (h, k). If slope of the line is m, show that k - y 1 = m (h - x 1).