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प्रश्न
Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km.
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उत्तर
By given condition, we drawn a figure in which every place are indicated with his coordinates and direction also.
We know that,
Distance between two points (x1, y1) and (x2, y2),
d = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
Now, distance between house and bank
= `sqrt((5 - 2)^2 + (8 - 4)^2`
= `sqrt((3)^2 + (4)^2`
= `sqrt(9 + 16)`
= `sqrt(25)`
= 5
Distance between bank and daughter's school
= `sqrt((13 - 5)^2 + (14 - 8)^2`
= `sqrt((8)^2 + (6)^2`
= `sqrt(64 + 36)`
= `sqrt(100)`
= 10
Distance between daughter's school and office
= `sqrt((13 - 13)^2 + (26 - 14)^2`
= `sqrt(0 + (12)^2`
= 12
Total distance (House + Bank + School + Office) travelled
= 5 + 10 + 12
= 27 units
Distance between house to offices
= `sqrt((13 - 2)^2 + (26 - 4)^2`
= `sqrt((11)^2 + (22)^2`
= `sqrt(121 + 484)`
= `sqrt(605)`
= 24.59
= 24.6 km
So, extra distance travelled by Ayush in reaching his office = 27 – 24.6 = 2.4 km.
Hence, the required extra distance travelled by Ayush is 2.4 km.
संबंधित प्रश्न
The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) and R(–3, 6), find the coordinates of P.
Find the value of x, if the distance between the points (x, – 1) and (3, 2) is 5.
Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area
If P and Q are two points whose coordinates are (at2 ,2at) and (a/t2 , 2a/t) respectively and S is the point (a, 0). Show that `\frac{1}{SP}+\frac{1}{SQ}` is independent of t.
Find the coordinates of the centre of the circle passing through the points (0, 0), (–2, 1) and (–3, 2). Also, find its radius.
Find the distance between the following pairs of points:
(−5, 7), (−1, 3)
Prove that the points A(1, 7), B(4, 2), C(−1, −1), and D(−4, 4) are the vertices of a square.
Find the centre of the circle passing through (6, -6), (3, -7) and (3, 3)
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 following set of point is collinear :
(5 , 5),(3 , 4),(-7 , -1)
Prove that the points (1 , 1) , (-1 , -1) and (`- sqrt 3 , sqrt 3`) are the vertices of an equilateral triangle.
A point P lies on the x-axis and another point Q lies on the y-axis.
Write the ordinate of point P.
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 point (11, –2) is equidistant from (4, –3) and (6, 3).
If the distance between the points (x, -1) and (3, 2) is 5, then the value of x 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 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.
A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?
