Advertisements
Advertisements
Question
The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x = ______.
Options
2
6
3
1
Advertisements
Solution
The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x = 6.
Explanation:
Let P(x1, y1) = P(2, 2) and Q(x2, y2) = Q(5, x)
Here, x1 = 2, y1 = 2, x2 = 5, y2 = x
By distance formula,
d(P, Q) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
∴ `5 = sqrt((5 - 2)^2 + (x - 2)^2)`
∴ `5 = sqrt(9 + x^2 - 4x + 4)`
∴ 52 = x2 – 4x + 13 ...[Squaring both sides]
∴ 25 = x2 – 4x + 13
∴ x2 – 4x + 13 – 25 = 0
∴ x2 – 4x – 12 = 0
∴ (x – 6) (x + 2) = 0
∴ x – 6 = 0 or x + 2 = 0
∴ x = 6 or x = –2
APPEARS IN
RELATED QUESTIONS
Find the distance between the following pairs of points:
(2, 3), (4, 1)
Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).
Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (–3, 4).
Find the distance between the following pair of points:
(a + b, b + c) and (a – b, c – b)
Find all possible values of y for which the distance between the points A(2, –3) and B(10, y) is 10 units.
Find the values of x for which the distance between the points P(x, 4) and Q(9, 10) is 10 units.
Find the distance of the following point from the origin :
(0 , 11)
ABC is an equilateral triangle . If the coordinates of A and B are (1 , 1) and (- 1 , -1) , find the coordinates of C.
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.
Show that the points A (5, 6), B (1, 5), C (2, 1) and D (6, 2) are the vertices of a square ABCD.
Given A = (x + 2, -2) and B (11, 6). Find x if AB = 17.
Point P (2, -7) is the centre of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of AB.
Calculate the distance between A (7, 3) and B on the x-axis whose abscissa is 11.
If the distance between the points (4, P) and (1, 0) is 5, then the value of p 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 ______.
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 y axis equidistant from B and C is ______.
The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).
The centre of a circle is (2a, a – 7). Find the values of a if the circle passes through the point (11, –9) and has diameter `10sqrt(2)` units.
Show that Alia's house, Shagun's house and library for an isosceles right triangle.
A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?
