Advertisements
Advertisements
प्रश्न
Calculate the distance between A (5, -3) and B on the y-axis whose ordinate is 9.
Advertisements
उत्तर
We know that any point on y-axis has coordinates of the form (0, y).
Ordinate of point B = 9
Since, B lies of y-axis, so its co-ordinates are (0, 9).
AB = `sqrt((0 -5)^2 + (9 + 3)^2)`
= `sqrt(25 + 144)`
= `sqrt(169)`
= 13 units
APPEARS IN
संबंधित प्रश्न
Show that the points (a, a), (–a, –a) and (– √3 a, √3 a) are the vertices of an equilateral triangle. Also find its area.
If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y
Find the co-ordinates of points of trisection of the line segment joining the point (6, –9) and the origin.
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.
Find the distance of the following point from the origin :
(0 , 11)
Find the distance between the origin and the point:
(-5, -12)
Show that the point (0, 9) is equidistant from the points (–4, 1) and (4, 1).
Show that A(1, 2), (1, 6), C(1 + 2`sqrt(3)`, 4) are vertices of an equilateral triangle.
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:
The coordinates of the centroid of ΔEHJ are ______.
What type of a quadrilateral do the points A(2, –2), B(7, 3), C(11, –1) and D(6, –6) taken in that order, form?
