Advertisements
Advertisements
प्रश्न
The length of a line segment is of 10 units and the coordinates of one end-point are (2, -3). If the abscissa of the other end is 10, find the ordinate of the other end.
Advertisements
उत्तर
The distance d between two points `(x_1, y_1)` and `(x_2, y_2)` is given by the formula
d = sqrt((x_1, x_2)^2 + (y_1 - y_2)^2)`
Here it is given that one end of a line segment has co−ordinates (2,-3). The abscissa of the other end of the line segment is given to be 10. Let the ordinate of this point be ‘y’.
So, the co−ordinates of the other end of the line segment is (10, y).
The distance between these two points is given to be 10 units.
Substituting these values in the formula for distance between two points we have,
`d = sqrt((2 - 10)^2 + (-3 - y)^2)`
`10 = sqrt((-8)^2 + (-3 - y)^2)`
Squaring on both sides of the equation we have,
`100 = (-8)^2 + (-3-y)^2`
`100 = 64 + 9 + y^2 + 6y`
`27 = y^2 + 6y`
We have a quadratic equation for ‘y’. Solving for the roots of this equation we have,
`y^2 + 6y - 27 = 0`
`y^2 + 9y - 3y - 27 = 0`
y(y + 9) -3(y + 9) = 0
(y + 9)(y - 3) = 0
The roots of the above equation are ‘−9’ and ‘3’
Thus the ordinates of the other end of the line segment could be -9 or 3
APPEARS IN
संबंधित प्रश्न
If A(4, 3), B(-1, y) and C(3, 4) are the vertices of a right triangle ABC, right-angled at A, then find the value of y.
Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.
Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(- 1, - 2), (1, 0), (- 1, 2), (- 3, 0)
If Q (0, 1) is equidistant from P (5, − 3) and R (x, 6), find the values of x. Also find the distance QR and PR.
Find all possible values of y for which distance between the points is 10 units.
Find the distance between the following pairs of point in the coordinate plane :
(7 , -7) and (2 , 5)
Find the distance of the following point from the origin :
(13 , 0)
Find the distance between the following point :
(sin θ , cos θ) and (cos θ , - sin θ)
Find the value of a if the distance between the points (5 , a) and (1 , 5) is 5 units .
Find the distance between the points (a, b) and (−a, −b).
Find the distance between the following pair of points:
`(sqrt(3)+1,1)` and `(0, sqrt(3))`
A point P (2, -1) is equidistant from the points (a, 7) and (-3, a). Find a.
Find a point on the y-axis which is equidistant from the points (5, 2) and (-4, 3).
By using the distance formula prove that each of the following sets of points are the vertices of a right angled triangle.
(i) (6, 2), (3, -1) and (- 2, 4)
(ii) (-2, 2), (8, -2) and (-4, -3).
Find distance between points O(0, 0) and B(– 5, 12)
If the distance between point L(x, 7) and point M(1, 15) is 10, then find the value of x
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 ______.
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).
Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).
