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.
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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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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.
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Question 4:Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
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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).
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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.
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Question 7:Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.
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Question 8:Find the value of x for which the points (x, – 1), (2,1) and (4, 5) are collinear.
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Question 9:Without using distance formula, show that points (– 2, – 1), (4, 0), (3, 3) and (–3, 2) are the vertices of a parallelogram.
EXERCISE 10.11. Draw a quadrilateral in the Cartes
Question 10:Find the angle between the x-axis and the line joining the points (3,–1) and (4,–2).
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Question 11:The slope of a line is double of the slope of another line. If tangent of the angle between them is 3 1 , find the slopes of the lines.
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Question 12:A line passes through (x1, y1) and (h, k). If slope of the line is m, show that k – y1 = m (h – x1).
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Question 13:If three points (h, 0), (a, b) and (0, k) lie on a line, show that + = 1 k b h a .
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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?
