NCERT Solutions
Class 11 - Mathematics - Chapter 9: STRAIGHT LINES

EXERCISE 9.1

Draw a quadrilateral in the Cartesian plane, whose vertices are \((-4,5), (0,7), (5,-5), (-4,-2)\). 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 \((x_1, y_1)\) and Q \((x_2, y_2)\) when (i) PQ is parallel to the y-axis, (ii) PQ is parallel to the x-axis.

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 \(30^\circ\) 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 the slope of another line. If tangent of the angle between them is \(\dfrac{1}{3}\), find the slopes of the lines.

A line passes through \((x_1, y_1)\) and \((h, k)\). If slope of the line is m, show that \(k - y_1 = m(h - x_1)\).