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P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is `x/a + y/b = 2`
Concept: undefined >> undefined
Point R (h, k) divides a line segment between the axes in the ratio 1:2. Find equation of the line.
Concept: undefined >> undefined
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By using the concept of equation of a line, prove that the three points (3, 0), (–2, –2) and (8, 2) are collinear.
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Find the values of q and p, if the equation x cos q + y sinq = p is the normal form of the line `sqrt3 x` + y + 2 = 0.
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Find the area of the triangle formed by the lines y – x = 0, x + y = 0 and x – k = 0.
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Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.
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If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find the value of m.
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A point is on the x-axis. What are its y-coordinates and z-coordinates?
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A point is in the XZ-plane. What can you say about its y-coordinate?
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The coordinates of points in the XY-plane are of the form _______.
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Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0, 4, 0) and (6, 0, 0).
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Find the coordinates of a point on y-axis which are at a distance of `5sqrt2` from the point P (3, –2, 5).
Concept: undefined >> undefined
A point R with x-coordinate 4 lies on the line segment joining the pointsP (2, –3, 4) and Q (8, 0, 10). Find the coordinates of the point R.
[Hint suppose R divides PQ in the ratio k: 1. The coordinates of the point R are given by `((8k + 2)/(k+1), (-3)/(k+1), (10k + 4)/(k+1))`
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If A and B be the points (3, 4, 5) and (–1, 3, –7), respectively, find the equation of the set of points P such that PA2 + PB2 = k2, where k is a constant.
Concept: undefined >> undefined
Write the negation of the following statements:
Chennai is the capital of Tamil Nadu.
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Write the negation of the following statements:
`sqrt2` is not a complex number.
Concept: undefined >> undefined
Write the negation of the following statements:
All triangles are not equilateral triangle.
Concept: undefined >> undefined
Write the negation of the following statements:
The number 2 is greater than 7.
Concept: undefined >> undefined
Write the negation of the following statements:
Every natural number is an integer.
Concept: undefined >> undefined
Are the following pairs of statements negations of each other?
The number x is not a rational number.
The number x is not an irrational number.
Concept: undefined >> undefined
