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.
APPEARS IN
संबंधित प्रश्न
If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible values of k?
Show that the points A (1, −2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.
Find the distance between the points:
P(a + b, a - b) and Q(a - b, a + b)
Find the distance between the following pair of points.
L(5, –8), M(–7, –3)
Determine whether the point is collinear.
R(0, 3), D(2, 1), S(3, –1)
Show that the ▢PQRS formed by P(2, 1), Q(–1, 3), R(–5, –3) and S(–2, –5) is a rectangle.
If A and B are the points (−6, 7) and (−1, −5) respectively, then the distance
2AB is equal to
Find the distance between the following pair of point in the coordinate plane :
(5 , -2) and (1 , 5)
Find the distance between the following pairs of point in the coordinate plane :
(4 , 1) and (-4 , 5)
Find the distance between the following point :
(sin θ , cos θ) and (cos θ , - sin θ)
Find the value of a if the distance between the points (5 , a) and (1 , 5) is 5 units .
Prove taht the points (-2 , 1) , (-1 , 4) and (0 , 3) are the vertices of a right - angled triangle.
Find the distance between the following pairs of points:
`(3/5,2) and (-(1)/(5),1(2)/(5))`
Find a point on the y-axis which is equidistant from the points (5, 2) and (-4, 3).
The distance between points P(–1, 1) and Q(5, –7) is ______.
Find distance between point A(7, 5) and B(2, 5).
Show that the points (0, –1), (8, 3), (6, 7) and (–2, 3) are vertices of a rectangle.
The points A(–1, –2), B(4, 3), C(2, 5) and D(–3, 0) in that order form a rectangle.
Read the following passage:
|
Use of mobile screen for long hours makes your eye sight weak and give you headaches. Children who are addicted to play "PUBG" can get easily stressed out. To raise social awareness about ill effects of playing PUBG, a school decided to start 'BAN PUBG' campaign, in which students are asked to prepare campaign board in the shape of a rectangle: One such campaign board made by class X student of the school is shown in the figure.
|
Based on the above information, answer the following questions:
- Find the coordinates of the point of intersection of diagonals AC and BD.
- Find the length of the diagonal AC.
-
- Find the area of the campaign Board ABCD.
OR - Find the ratio of the length of side AB to the length of the diagonal AC.
- Find the area of the campaign Board ABCD.
The distance of the point (5, 0) from the origin is ______.
