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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).
पर्याय
True
False
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)`
Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.
Find the distance between the following pairs of points:
(2, 3), (4, 1)
Given a line segment AB joining the points A(–4, 6) and B(8, –3). Find
1) The ratio in which AB is divided by y-axis.
2) Find the coordinates of the point of intersection.
3) The length of AB.
If the point P(x, y ) is equidistant from the points A(5, 1) and B (1, 5), prove that x = y.
Find the distance of the following point from the origin :
(0 , 11)
Find the point on the x-axis equidistant from the points (5,4) and (-2,3).
If the distance between the points (x, -1) and (3, 2) is 5, then the value of x 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 point on x axis equidistant from I and E is ______.
Show that Alia's house, Shagun's house and library for an isosceles right triangle.
