Straight Lines

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 $P(x_1, y_1)$ and $Q(x_2, y_2)$ when:

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 of the slope of another line. If tangent of the angle between them is $\frac{1}{3}$, 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 $k - y_1 = m(h - x_1)$.

Write the equations for the $x$-and $y$-axes.

In Exercises 1 to 8, find the equation of the line which satisfy the given conditions: Passing through the point $(-4, 3)$ with slope $\frac{1}{2}$.

In Exercises 1 to 8, find the equation of the line which satisfy the given conditions: Passing through $(0, 0)$ with slope $m$.

In Exercises 1 to 8, find the equation of the line which satisfy the given conditions: Passing through $(2, 2\sqrt{3})$ and inclined with the $x$-axis at an angle of $75^\circ$.

In Exercises 1 to 8, find the equation of the line which satisfy the given conditions: Intersecting the $x$-axis at a distance of 3 units to the left of origin with slope $-2$.

In Exercises 1 to 8, find the equation of the line which satisfy the given conditions: Intersecting the $y$-axis at a distance of 2 units above the origin and making an angle of $30^\circ$ with positive direction of the $x$-axis.

In Exercises 1 to 8, find the equation of the line which satisfy the given conditions: Passing through the points $(-1, 1)$ and $(2, -4)$.

The vertices of $\Delta PQR$ are $P(2, 1)$, $Q(-2, 3)$ and $R(4, 5)$. Find equation of the median through the vertex $R$.

Find the equation of the line passing through $(-3, 5)$ and perpendicular to the line through the points $(2, 5)$ and $(-3, 6)$.