Advertisements
Advertisements
प्रश्न
The distance between points P(–1, 1) and Q(5, –7) is ______.
विकल्प
11 cm
10 cm
5 cm
7 cm
Advertisements
उत्तर
The distance between points P(–1, 1) and Q(5, –7) is 10 cm.
Explanation:
Let P(x1, y1) = P(–1, 1) and Q(x2, y2) = Q(5, –7)
Here, x1 = –1, y1 = 1, x2 = 5, y2 = –7
By distance formula,
d(P, Q) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
= `sqrt([5 - (-1)]^2 + (-7 - 1)^2)`
= `sqrt(36 + 64)`
= `sqrt(100)`
= 10 cm
APPEARS IN
संबंधित प्रश्न
If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay.
Find the value of x, if the distance between the points (x, – 1) and (3, 2) is 5.
If P (2, – 1), Q(3, 4), R(–2, 3) and S(–3, –2) be four points in a plane, show that PQRS is a rhombus but not a square. Find the area of the rhombus
If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y
Find the distance between the following pair of points:
(asinα, −bcosα) and (−acos α, bsin α)
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 between the points:
A(9, 3) and B(15, 11)
Find the distance between the points:
A(7, –4) and B(–5, 1)
If P(x, y) is equidistant from the points A(7, 1) and B(3, 5), find the relation between x and y.
Determine whether the point is collinear.
R(0, 3), D(2, 1), S(3, –1)
Find the distance between the following pairs of point in the coordinate plane :
(4 , 1) and (-4 , 5)
Find the relation between a and b if the point P(a ,b) is equidistant from A (6,-1) and B (5 , 8).
Prove that the points (4 , 6) , (- 1 , 5) , (- 2, 0) and (3 , 1) are the vertices of a rhombus.
ABC is an equilateral triangle . If the coordinates of A and B are (1 , 1) and (- 1 , -1) , find the coordinates of C.
Show that the points P (0, 5), Q (5, 10) and R (6, 3) are the vertices of an isosceles triangle.
Calculate the distance between A (5, -3) and B on the y-axis whose ordinate is 9.
Using distance formula decide whether the points (4, 3), (5, 1) and (1, 9) are collinear or not.
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 ______.
What type of a quadrilateral do the points A(2, –2), B(7, 3), C(11, –1) and D(6, –6) taken in that order, form?
