Advertisements
Advertisements
प्रश्न
Find distance between point Q(3, –7) and point R(3, 3)
Solution: Suppose Q(x1, y1) and point R(x2, y2)
x1 = 3, y1 = –7 and x2 = 3, y2 = 3
Using distance formula,
d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `sqrt(square - 100)`
∴ d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `square`
Advertisements
उत्तर
Suppose Q(x1, y1) and point R(x2, y2)
x1 = 3, y1 = –7 and x2 = 3, y2 = 3
Using distance formula,
d(Q, R) = \[\sqrt{\boxed{(x_2 - x_1)^2 + (y_2 - y_1)^2}}\]
= `sqrt((3 - 3)^2 - [3 - (- 7)]^2`
= `sqrt(0^2 + (10)^2)`
∴ d(Q, R) = \[\sqrt{\boxed{0} - 100}\]
∴ d(Q, R) = \[\sqrt{\boxed{100}}\]
∴ d(Q, R) = \[\boxed{10}\]
APPEARS IN
संबंधित प्रश्न
If the opposite vertices of a square are (1, – 1) and (3, 4), find the coordinates of the remaining angular points.
Find the distance between the following pairs of points:
(2, 3), (4, 1)
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.
Find the distance between the following pair of points:
(-6, 7) and (-1, -5)
Prove that the points A(1, 7), B(4, 2), C(−1, −1), and D(−4, 4) are the vertices of a square.
Two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two
vertices.
Using the distance formula, show that the given points are collinear:
(1, –1), (5, 2) and (9, 5)
Find the distance between the following pairs of point in the coordinate plane :
(4 , 1) and (-4 , 5)
Find the distance of the following point from the origin :
(5 , 12)
Find the distance of a point (12 , 5) from another point on the line x = 0 whose ordinate is 9.
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.
Prove that the points P (0, -4), Q (6, 2), R (3, 5) and S (-3, -1) are the vertices of a rectangle PQRS.
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
Show that the point (11, –2) is equidistant from (4, –3) and (6, 3).
Show that A(1, 2), (1, 6), C(1 + 2`sqrt(3)`, 4) are vertices of an equilateral triangle.
The equation of the perpendicular bisector of line segment joining points A(4,5) and B(-2,3) 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 ______.
Find a point which is equidistant from the points A(–5, 4) and B(–1, 6)? How many such points are there?
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.
What is the distance of the point (– 5, 4) from the origin?
