Advertisements
Advertisements
प्रश्न
Find the distances between the following point.
A(a, 0), B(0, a)
Advertisements
उत्तर
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
संबंधित प्रश्न
If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also, find the length of AB.
Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.
Prove that the points (–3, 0), (1, –3) and (4, 1) are the vertices of an isosceles right angled triangle. Find the area of this triangle
Find the distance between the following pairs of points:
(2, 3), (4, 1)
If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible values of k?
Prove that the points A(1, 7), B (4, 2), C(−1, −1) D (−4, 4) are the vertices of a square.
Find the distance between the points
P(a sin ∝,a cos ∝ )and Q( acos ∝ ,- asin ∝)
Using the distance formula, show that the given points are collinear:
(1, -1), (5, 2) and (9, 5)
Find the distance between the following pair of point.
P(–5, 7), Q(–1, 3)
Find the value of y for which the distance between the points A (3, −1) and B (11, y) is 10 units.
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.
Find the value of a if the distance between the points (5 , a) and (1 , 5) is 5 units .
Prove that the points (0,3) , (4,3) and `(2, 3+2sqrt 3)` are the vertices of an equilateral triangle.
A point P lies on the x-axis and another point Q lies on the y-axis.
If the abscissa of point P is -12 and the ordinate of point Q is -16; calculate the length of line segment PQ.
Show that the points (a, a), (-a, -a) and `(-asqrt(3), asqrt(3))` are the vertices of an equilateral triangle.
Find distance between points O(0, 0) and B(– 5, 12)
A circle drawn with origin as the centre passes through `(13/2, 0)`. The point which does not lie in the interior of the circle is ______.
∆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).
Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km.
If the point A(2, – 4) is equidistant from P(3, 8) and Q(–10, y), find the values of y. Also find distance PQ.
