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प्रश्न
Point P(0, 2) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A(–1, 1) and B(3, 3).
विकल्प
True
False
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उत्तर
This statement is False.
Explanation:
We know that, the points lying on perpendicular bisector of the line segment joining the two points is equidistant from the two points.
i.e., PA should be equals to the PB.
Using distance formula,
d = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
PA = `sqrt([-4 - (4)]^2 + (6 - 2)^2`
PA = `sqrt((0)^2 + (4)^2` = 4
PB = `sqrt([-4 - 4]^2 + (-6 - 2)^2`
PB = `sqrt(0^2 + (-8)^2` = 8
∵ PA ≠ PB
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संबंधित प्रश्न
Find the distance between two points
(i) P(–6, 7) and Q(–1, –5)
(ii) R(a + b, a – b) and S(a – b, –a – b)
(iii) `A(at_1^2,2at_1)" and " B(at_2^2,2at_2)`
Prove that the points (–3, 0), (1, –3) and (4, 1) are the vertices of an isosceles right angled triangle. Find the area of this triangle
The value of 'a' for which of the following points A(a, 3), B (2, 1) and C(5, a) a collinear. Hence find the equation of the line.
If A (-1, 3), B (1, -1) and C (5, 1) are the vertices of a triangle ABC, find the length of the median through A.
Given a triangle ABC in which A = (4, −4), B = (0, 5) and C = (5, 10). A point P lies on BC such that BP : PC = 3 : 2. Find the length of line segment AP.
Find the co-ordinates of points of trisection of the line segment joining the point (6, –9) and the origin.
Find all possible values of x for which the distance between the points
A(x,-1) and B(5,3) is 5 units.
`" Find the distance between the points" A ((-8)/5,2) and B (2/5,2)`
Determine whether the point is collinear.
R(0, 3), D(2, 1), S(3, –1)
Find the distances between the following point.
A(a, 0), B(0, a)
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(-2, -3), B(-1, 0) and C(7, -6) are the vertices of a triangle. Find the circumcentre and the circumradius of the triangle.
PQR is an isosceles triangle . If two of its vertices are P (2 , 0) and Q (2 , 5) , find the coordinates of R if the length of each of the two equal sides is 3.
Find the distance between the origin and the point:
(8, −15)
A point P (2, -1) is equidistant from the points (a, 7) and (-3, a). Find a.
Show that the point (11, –2) is equidistant from (4, –3) and (6, 3).
Seg OA is the radius of a circle with centre O. The coordinates of point A is (0, 2) then decide whether the point B(1, 2) is on the circle?
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:
What are the coordinates of the position of a player Q such that his distance from K is twice his distance from E and K, Q and E are collinear?
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)`
