Ncert Solutions for Class 11 Mathematics Chapter 10 Straight lines Exercise Solutions 10.1

14 1. Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area.   2. The base of an equilateral triangle with side 2a lies along the yaxis such that the midpoint of the base is at the origin. Find vertices of the triangle.   3. Find the distance between P (x1, y1
and Q (x2, y2) when : (i) PQ is parallel to theyaxis, (ii) PQ is parallel to the xaxis.
  4. Find a point on the xaxis, which is equidistant from the points (7, 6) and (3, 4).
  5. Find the slope of a line, which passes through the origin, and the midpoint of the line segment joining the points P (0, – 4) and B (8, 0).   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.   7. Find the slope of the line, which makes an angle of 30° with the positive direction
of yaxis measured anticlockwise.   8. Find the value of x for which the points (x, – 1), (2,1) and (4, 5) are collinear.
  9. Without using distance formula, show that points (– 2, – 1), (4, 0), (3, 3) and (–3, 2) are the vertices of a parallelogram.
  10. Find the angle between the xaxis and the line joining the points (3,–1) and (4,–2).
 
 11. The slope of a line is double of the slope of another line. If tangent of the angle between them is 1/3, find the slopes of the lines.
  12. A line passes through (x1, y1) and (h, k). If slope of the line is m, show that k – y1 = m (h – x1).   13. If three points (h, 0), (a, b) and (0, k) lie on a line, show that
a/h + b/k = 0   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?  
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