We realize that, the line AB goes through focuses\[\mathbf{A}\text{ }\left( \mathbf{1985},\text{ }\mathbf{92} \right)\text{ }\mathbf{and}\text{ }\mathbf{B}\text{ }\left( \mathbf{1995},\text{...
If three points (h, 0), (a, b) and (0, k) lie on a line, show that a/h + b/k = 1
Allow us to consider if the given focuses \[\mathbf{A}\text{ }\left( \mathbf{h},\text{ }\mathbf{0} \right),\text{ }\mathbf{B}\text{ }\left( \mathbf{a},\text{ }\mathbf{b} \right)\text{...
A line passes through (x1, y1) and (h, k). If slope of the line is m, show that k – y1 = m (h – x1).
Given: the slant of the line is 'm' The slant of the line going through \[\left( \mathbf{x1},\text{ }\mathbf{y1} \right)\text{ }\mathbf{and}\text{ }\left( \mathbf{h},\text{ }\mathbf{k} \right)\]...
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.
Allow us to consider 'm1' and 'm' be the incline of the two given lines to such an extent that \[\mathbf{m1}\text{ }=\text{ }\mathbf{2m}\] We realize that in case θ is the point somewhere within l1...
Find the angle between the x-axis and the line joining the points (3, –1) and (4, –2).
Slope of the line joining the focuses \[\left( \mathbf{3},\text{ }-\text{ }\mathbf{1} \right)\text{ }\mathbf{and}\text{ }\left( \mathbf{4},\text{ }-\text{ }\mathbf{2} \right)\] is given by ...
Without using distance formula, show that points (– 2, – 1), (4, 0), (3, 3) and (–3, 2) are the vertices of a parallelogram
Leave the given point alone \[\mathbf{A}\text{ }\left( -\text{ }\mathbf{2},\text{ }-\text{ }\mathbf{1} \right)\text{ },\text{ }\mathbf{B}\text{ }\left( \mathbf{4},\text{ }\mathbf{0} \right)\text{...
Find the value of x for which the points (x, – 1), (2, 1) and (4, 5) are collinear.
On the off chance that the focuses \[\left( \mathbf{x},\text{ }\text{ }\mathbf{1} \right),\text{ }\left( \mathbf{2},\text{ }\mathbf{1} \right)\text{ }\mathbf{and}\text{ }\left( \mathbf{4},\text{...
Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.
We realize that, if a line makes a point of \[\mathbf{30}{}^\circ \] with the positive bearing of y-pivot estimated against clock-wise , then, at that point, the point made by the line with the...
Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right-angled triangle.
The vertices of the given triangle are \[\left( \mathbf{4},\text{ }\mathbf{4} \right),\text{ }\left( \mathbf{3},\text{ }\mathbf{5} \right)\text{ }\mathbf{and}\text{ }\left( \text{ }\mathbf{1},\text{...
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)
The co-ordinates of mid-point of the line portion joining the focuses \[\mathbf{P}\text{ }\left( \mathbf{0},\text{ }\text{ }\mathbf{4} \right)\text{ }\mathbf{and}\text{ }\mathbf{B}\text{ }\left(...
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
Allow us to consider \[\left( \mathbf{a},\text{ }\mathbf{0} \right)\] be the point on the x-hub that is equidistant from the point \[\left( \mathbf{7},\text{ }\mathbf{6} \right)\] and \[\left(...
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
Given: Focuses \[\mathbf{P}\text{ }\left( \mathbf{x1},\text{ }\mathbf{y1} \right)\text{ }\mathbf{and}\text{ }\mathbf{Q}\left( \mathbf{x2},\text{ }\mathbf{y2} \right)\] (i) When PQ is corresponding...
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
Allow us to consider ABC be the given symmetrical triangle with side 2a. Where, \[\mathbf{AB}\text{ }=\text{ }\mathbf{BC}\text{ }=\text{ }\mathbf{AC}\text{ }=\text{ }\mathbf{2a}\] In the above...
Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.
Leave ABCD alone the given quadrilateral with vertices \[\mathbf{A}\text{ }\left( -\text{ }\mathbf{4},\mathbf{5} \right)\text{ },\text{ }\mathbf{B}\text{ }\left( \mathbf{0},\mathbf{7} \right),\text{...