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प्रश्न
Find the distance between the following pairs of points:
(a, b), (−a, −b)
Find the distance between the following pairs of points:
(-a, -b) and (a, b)
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उत्तर
Distance between (a, b) and (−a, −b) is given by
l = `sqrt((a-(-a))^2+(b-(-b))^2)`
= `sqrt((2a)^2 + (2b)^2)`
= `sqrt(4a^2+4b^2)`
= `2sqrt(a^2 + b^2)`
संबंधित प्रश्न
Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.
An equilateral triangle has two vertices at the points (3, 4) and (−2, 3), find the coordinates of the third vertex.
Find the distance between the points:
P(a + b, a - b) and Q(a - b, a + b)
Find all possible values of y for which distance between the points is 10 units.
Using the distance formula, show that the given points are collinear:
(6, 9), (0, 1) and (-6, -7)
If P (x , y ) is equidistant from the points A (7,1) and B (3,5) find the relation between x and y
Determine whether the points are collinear.
P(–2, 3), Q(1, 2), R(4, 1)
Show that the points A(1, 2), B(1, 6), C(1 + 2`sqrt3`, 4) are vertices of an equilateral triangle.
Find the distance between the following pair of point in the coordinate plane.
(1 , 3) and (3 , 9)
Find the distance of the following point from the origin :
(5 , 12)
Find the value of a if the distance between the points (5 , a) and (1 , 5) is 5 units .
Prove that the points (a, b), (a + 3, b + 4), (a − 1, b + 7) and (a − 4, b + 3) are the vertices of a parallelogram.
Prove that the points (0 , -4) , (6 , 2) , (3 , 5) and (-3 , -1) are the vertices of a rectangle.
Find the distance between the points (a, b) and (−a, −b).
Find the distance between the following pairs of points:
(–3, 6) and (2, –6)
Calculate the distance between the points P (2, 2) and Q (5, 4) correct to three significant figures.
Find the distance of the following points from origin.
(a+b, a-b)
KM is a straight line of 13 units If K has the coordinate (2, 5) and M has the coordinates (x, – 7) find the possible value of x.
The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x ______
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 point A(7, 5) and B(2, 5)
Find distance of point A(6, 8) from origin
Find distance CD where C(– 3a, a), D(a, – 2a)
The distance between the points (0, 5) and (–5, 0) is ______.
The coordinates of the point which is equidistant from the three vertices of the ΔAOB as shown in the figure is ______.
Case Study -2
A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.
It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.
Each team plays with 11 players on the field during the game including the goalie. Positions you might play include -
- Forward: As shown by players A, B, C and D.
- Midfielders: As shown by players E, F and G.
- Fullbacks: As shown by players H, I and J.
- Goalie: As shown by player K.
Using the picture of a hockey field below, answer the questions that follow:
If a player P needs to be at equal distances from A and G, such that A, P and G are in straight line, then position of P will be given by ______.
∆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).
Points A(4, 3), B(6, 4), C(5, –6) and D(–3, 5) are the vertices of a parallelogram.
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In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.
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Based on the above information answer the following questions using the coordinate geometry.
- Find the distance between Lucknow (L) to Bhuj (B).
- If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
- Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P)
[OR]
Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).
A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?
