Advertisements
Advertisements
Question
A point P lies on the x-axis and another point Q lies on the y-axis.
If the abscissa of point P is -12 and the ordinate of point Q is -16; calculate the length of line segment PQ.
Solution
The co-ordinates of P and Q are (-12, 0) and (0, -16) respectively.
PQ = `sqrt((-12 - 0)^2 + (0 + 16)^2)`
= `sqrt(144 + 256)`
= `sqrt(400)`
= 20
APPEARS IN
RELATED QUESTIONS
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(−3, 5), (3, 1), (0, 3), (−1, −4)
If a≠b≠0, prove that the points (a, a2), (b, b2) (0, 0) will not be collinear.
If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y
Find the value of a when the distance between the points (3, a) and (4, 1) is `sqrt10`
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.
Using the distance formula, show that the given points are collinear:
(-2, 5), (0,1) and (2, -3)
`" Find the distance between the points" A ((-8)/5,2) and B (2/5,2)`
Find the distance of the following point from the origin :
(5 , 12)
Find the coordinate of O , the centre of a circle passing through A (8 , 12) , B (11 , 3), and C (0 , 14). Also , find its radius.
Prove that the points (6 , -1) , (5 , 8) and (1 , 3) are the vertices of an isosceles triangle.
Prove that the points (1 , 1) , (-1 , -1) and (`- sqrt 3 , sqrt 3`) are the vertices of an equilateral triangle.
A(2, 5), B(-2, 4) and C(-2, 6) are the vertices of a triangle ABC. Prove that ABC is an isosceles triangle.
The length of line PQ is 10 units and the co-ordinates of P are (2, -3); calculate the co-ordinates of point Q, if its abscissa is 10.
Find the point on y-axis whose distances from the points A (6, 7) and B (4, -3) are in the ratio 1: 2.
The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x ______
Show that A(1, 2), (1, 6), C(1 + 2 `sqrt(3)`, 4) are vertices of a equilateral triangle
The point which divides the lines segment joining the points (7, -6) and (3, 4) in ratio 1 : 2 internally lies in the ______.
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)`
A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?
