Draw a quadrilateral in the Cartesian plane, whose vertices are \((-4,5), (0,7), (5,-5), (-4,-2)\). Also, find its area.
\(\dfrac{121}{2}\) square unit.
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.
(0, a), (0, -a) and \((-\sqrt{3} a, 0)\) or (0, a), (0, -a), and \((\sqrt{3} a, 0)\)
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.
(i) \(|y_2 - y_1|\), (ii) \(|x_2 - x_1|\)
Find a point on the x-axis which is equidistant from the points (7, 6) and (3, 4).
\(\left(\dfrac{15}{2}, 0\right)\)
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).
\(-\dfrac{1}{2}\)
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.
\(-\sqrt{3}\)
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).
135°
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.
1 and 2, or \(\dfrac{1}{2}\) and 1, or −1 and −2, or −\(\dfrac{1}{2}\) and −1
A line passes through \((x_1, y_1)\) and \((h, k)\). If slope of the line is m, show that \(k - y_1 = m(h - x_1)\).