Advertisements
Advertisements
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.
Advertisements
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
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 a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (–3, 4).
Show that the points A (1, –2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.
Show that the quadrilateral whose vertices are (2, −1), (3, 4) (−2, 3) and (−3,−2) is a rhombus.
Find the distance between the following pair of point.
T(–3, 6), R(9, –10)
Find the distance between the following pair of point in the coordinate plane.
(1 , 3) and (3 , 9)
Find the distance between the following point :
(p+q,p-q) and (p-q, p-q)
ABCD is a square . If the coordinates of A and C are (5 , 4) and (-1 , 6) ; find the coordinates of B and D.
A point A is at a distance of `sqrt(10)` unit from the point (4, 3). Find the co-ordinates of point A, if its ordinate is twice its abscissa.
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.
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.
KM is a straight line of 13 units If K has the coordinate (2, 5) and M has the coordinates (x, – 7) find the possible value of x.
If the point (x, y) is at equidistant from the point (a + b, b – a) and (a-b, a + b). Prove that ay = bx.
Find distance between point A(7, 5) and B(2, 5).
The point which divides the lines segment joining the points (7, -6) and (3, 4) in ratio 1 : 2 internally lies in the ______.
The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.
Find the distance between the points O(0, 0) and P(3, 4).
Read the following passage:
|
Alia and Shagun are friends living on the same street in Patel Nagar. Shagun's house is at the intersection of one street with another street on which there is a library. They both study in the same school and that is not far from Shagun's house. Suppose the school is situated at the point O, i.e., the origin, Alia's house is at A. Shagun's house is at B and library is at C. |
Based on the above information, answer the following questions.
- How far is Alia's house from Shagun's house?
- How far is the library from Shagun's house?
- Show that for Shagun, school is farther compared to Alia's house and library.
OR
Show that Alia’s house, shagun’s house and library for an isosceles right triangle.
