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प्रश्न
A line segment is of length 10 units. If the coordinates of its one end are (2, −3) and the abscissa of the other end is 10, then its ordinate is
विकल्प
9, 6
3, −9
−3, 9
9, −6
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उत्तर
It is given that distance between P (2,−3) and Q(10 , y) is 10.
In general, the distance between A(x1 , y1) and B(x2 , y2 ) is given by,
`AB^2 = (x_2 - x_1 )^2 + (y_2 - y_1 )^2`
So,
`10^2 = (10 - 2)^2 + (y + 3)^2`
On further simplification,
`(y + 3 )^2 = 36`
`y = -3+-6`
`= -9 , 3`
We will neglect the negative value. So,
` y= -9 , 3`
संबंधित प्रश्न
(Street Plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.
All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines.
There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:
- how many cross - streets can be referred to as (4, 3).
- how many cross - streets can be referred to as (3, 4).
On which axis do the following points lie?
P(5, 0)
Find the distance between the following pair of points:
(a, 0) and (0, b)
Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.
The three vertices of a parallelogram are (3, 4) (3, 8) and (9, 8). Find the fourth vertex.
Find the equation of the perpendicular bisector of the line segment joining points (7, 1) and (3,5).
The points (3, -4) and (-6, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (-1, -3). Find the coordinates of the fourth vertex.
In what ratio is the line segment joining the points (-2,-3) and (3, 7) divided by the y-axis? Also, find the coordinates of the point of division.
If A and B are (1, 4) and (5, 2) respectively, find the coordinates of P when AP/BP = 3/4.
Find the centroid of ΔABC whose vertices are A(2,2) , B (-4,-4) and C (5,-8).
Find the ratio in which the line segment joining the points A(3, −3) and B(−2, 7) is divided by the x-axis. Also, find the coordinates of the point of division.
Write the coordinates of a point on X-axis which is equidistant from the points (−3, 4) and (2, 5).
The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ) is
If (x , 2), (−3, −4) and (7, −5) are collinear, then x =
The distance of the point (4, 7) from the x-axis is
What is the form of co-ordinates of a point on the X-axis?
Any point on the line y = x is of the form ______.
If segment AB is parallel Y-axis and coordinates of A are (1, 3), then the coordinates of B are ______
Point P(– 4, 2) lies on the line segment joining the points A(– 4, 6) and B(– 4, – 6).
If the points P(1, 2), Q(0, 0) and R(x, y) are collinear, then find the relation between x and y.
Given points are P(1, 2), Q(0, 0) and R(x, y).
The given points are collinear, so the area of the triangle formed by them is `square`.
∴ `1/2 |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| = square`
`1/2 |1(square) + 0(square) + x(square)| = square`
`square + square + square` = 0
`square + square` = 0
`square = square`
Hence, the relation between x and y is `square`.
