Advertisements
Advertisements
Question
Find the distances between the following point.
A(a, 0), B(0, a)
Advertisements
Solution
A(a, 0), B(0, a)
\[AB = \sqrt{\left( 0 - a \right)^2 + \left( a - 0 \right)^2}\]
\[ = \sqrt{a^2 + a^2}\]
\[ = \sqrt{2 a^2}\]
\[ = a\sqrt{2}\]
APPEARS IN
RELATED QUESTIONS
If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay
Show that the points (a, a), (–a, –a) and (– √3 a, √3 a) are the vertices of an equilateral triangle. Also find its area.
Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.
Find the distance between the following pairs of points:
(−5, 7), (−1, 3)
If Q (0, 1) is equidistant from P (5, − 3) and R (x, 6), find the values of x. Also find the distance QR and PR.
If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y
Using the distance formula, show that the given points are collinear:
(1, -1), (5, 2) and (9, 5)
Find the value of y for which the distance between the points A (3, −1) and B (11, y) is 10 units.
Prove that the following set of point is collinear :
(4, -5),(1 , 1),(-2 , 7)
Find the coordinates of O, the centre passing through A( -2, -3), B(-1, 0) and C(7, 6). Also, find its radius.
A point P lies on the x-axis and another point Q lies on the y-axis.
Write the ordinate of point P.
Show that the points A (5, 6), B (1, 5), C (2, 1) and D (6, 2) are the vertices of a square ABCD.
Point P (2, -7) is the center of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of: AT

Give the relation that must exist between x and y so that (x, y) is equidistant from (6, -1) and (2, 3).
Find distance between point A(–1, 1) and point B(5, –7):
Solution: Suppose A(x1, y1) and B(x2, y2)
x1 = –1, y1 = 1 and x2 = 5, y2 = – 7
Using distance formula,
d(A, B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
∴ d(A, B) = `sqrt(square +[(-7) + square]^2`
∴ d(A, B) = `sqrt(square)`
∴ d(A, B) = `square`
∆ABC with vertices A(–2, 0), B(2, 0) and C(0, 2) is similar to ∆DEF with vertices D(–4, 0), E(4, 0) and F(0, 4).
The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).
Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).
The distance of the point (5, 0) from the origin is ______.
A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?
