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प्रश्न
Find the distance between the following pairs of point.
W `((- 7)/2 , 4)`, X (11, 4)
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उत्तर
Let the co-ordinates of point W are (x1, y1) and of point X are (x2, y2)
`((-7)/2,4)` = (x1, y1)
(11, 4) = (x2, y2)
d (W, X) = `sqrt((x_2-x_1)^2+(y_2-y_1)^2)`
= `sqrt((11-(-7/2))^2+(4-4)^2`
= `sqrt((11+7/2)^2+0)`
= `(11 + 7/2)`
= `11/1+7/2`
= `(22+7)/2`
= `29/2`
= 14.5
∴ Distance between points W and X is 14.5.
संबंधित प्रश्न
If P and Q are two points whose coordinates are (at2 ,2at) and (a/t2 , 2a/t) respectively and S is the point (a, 0). Show that `\frac{1}{SP}+\frac{1}{SQ}` is independent of t.
If a ≠ b ≠ 0, prove that the points (a, a2), (b, b2) (0, 0) will not be collinear.
Find the circumcenter of the triangle whose vertices are (–2, –3), (–1, 0), (7, –6).
A(–8, 0), B(0, 16) and C(0, 0) are the vertices of a triangle ABC. Point P lies on AB and Q lies on AC such that AP : PB = 3 : 5 and AQ : QC = 3 : 5. Show that : PQ = `3/8` BC.
Find the distance between the points:
A(9, 3) and B(15, 11)
Find the distance between the following pair of points.
L(5, –8), M(–7, –3)
Distance of point (−3, 4) from the origin is ______.
Find the distance of the following point from the origin :
(8 , 15)
Find the distance of a point (7 , 5) from another point on the x - axis whose abscissa is -5.
Prove taht the points (-2 , 1) , (-1 , 4) and (0 , 3) are the vertices of a right - angled triangle.
Find the distance between the origin and the point:
(8, −15)
Calculate the distance between A (7, 3) and B on the x-axis whose abscissa is 11.
Find the distance of the following points from origin.
(a cos θ, a sin θ).
Show that the quadrilateral with vertices (3, 2), (0, 5), (- 3, 2) and (0, -1) is a square.
The distance between points P(–1, 1) and Q(5, –7) is ______.
Find distance of point A(6, 8) from origin.
The point which lies on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) 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:
The coordinates of the centroid of ΔEHJ are ______.
Find the points on the x-axis which are at a distance of `2sqrt(5)` from the point (7, – 4). How many such points are there?
