Advertisements
Advertisements
प्रश्न
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`
Advertisements
उत्तर
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) = \[\sqrt{\boxed{[5 - (-1)]^2} + [(-7) + \boxed{-1}]^2}\]
∴ d(A, B) = `sqrt(6^2 + (-8)^2`
∴ d(A, B) = `sqrt(36 + 64)`
∴ d(A, B) = \[\sqrt{\boxed{100}}\]
∴ d(A, B) = \[\boxed{10 \phantom{.}\text{units}}\]
APPEARS IN
संबंधित प्रश्न
If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b). Prove that bx = ay.
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.
Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.
In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes, Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees.
Using distance formula, find which of them is correct.

Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(−3, 5), (3, 1), (0, 3), (−1, −4)
Find the distance of the following points from the origin:
C(–4, –6)
Using the distance formula, show that the given points are collinear:
(6, 9), (0, 1) and (–6, –7)
Find the distance between the following pair of points.
L(5, –8), M(–7, –3)
Determine whether the points are collinear.
L(–2, 3), M(1, –3), N(5, 4)
Show that the ▢PQRS formed by P(2, 1), Q(–1, 3), R(–5, –3) and S(–2, –5) is a rectangle.
Find the distance between P and Q if P lies on the y - axis and has an ordinate 5 while Q lies on the x - axis and has an abscissa 12 .
Prove that the points (1 ,1),(-4 , 4) and (4 , 6) are the certices of an isosceles triangle.
Prove that the points (4 , 6) , (- 1 , 5) , (- 2, 0) and (3 , 1) are the vertices of a rhombus.
Find the distance between the origin and the point:
(-8, 6)
A point A is at a distance of `sqrt(10)` unit from the point (4, 3). Find the co-ordinates of point A, if its ordinate is twice its abscissa.
Find the point on y-axis whose distances from the points A (6, 7) and B (4, -3) are in the ratio 1: 2.
Calculate the distance between A (7, 3) and B on the x-axis, whose abscissa is 11.
Give the relation that must exist between x and y so that (x, y) is equidistant from (6, -1) and (2, 3).
If the length of the segment joining point L(x, 7) and point M(1, 15) is 10 cm, then the value of x is ______.
Find distance between points P(– 5, – 7) and Q(0, 3).
By distance formula,
PQ = `sqrt(square + (y_2 - y_1)^2`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(125)`
= `5sqrt(5)`
