Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Coordinates of A (2, 3) – Alia's house
Coordinates of B (2, 1) – Shagun's house
Coordfuates of C (4, 1) – Library
i. AB = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
= `sqrt((2 - 2)^2 + (1 - 3)^2`
= `sqrt((0)^2 + (-2)^2`
AB = `sqrt(0 + 4)`
= `sqrt(4)` unit
= 2 units
Alia's house from shagun's house is 2 units
ii. C(4, 1), B(2, 1)
CB = `sqrt((2 - 4)^2 + (1 - 1)^2`
= `sqrt((-2)^2 + 0^2`
= `sqrt(4 + 0)`
= `sqrt(4)`
= 2 unit
iii. O(0, 0), B(2, 1)
OB = `sqrt((2 - 0)^2 + (1 - 0)^2`
= `sqrt(2^2 + 1^2)`
= `sqrt(4 + 1)`
= `sqrt(5)` units
Distance between Alia's house and Shagun's house, AB = 2 units
Distance between Library and Shagun's house, CB = 2 units
OB is greater than AB and CB,
For shagun, school [O] is farther than Alia's house [A] and Library [C]
OR
C(4, 1), A(2, 3)
CA = `sqrt((2 - 4)^2 + (3 - 1)^2`
= `sqrt((-2)^2 + 2^2`
= `sqrt(4 + 4)`
= `sqrt(8)`
= `2sqrt(2)` units
AC2 = 8
Distance between Alia’s house and Shagun’s house, AB = 2 units
Distance between Library and Shagun’s house, CB = 2 units
AB2 + BC2
= 22 + 22
= 4 + 4
= 8
= AC2
Therefore A, B and C form an isosceles right triangle.
APPEARS IN
संबंधित प्रश्न
Find the distance between the following pairs of points:
(a, b), (−a, −b)
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(- 1, - 2), (1, 0), (- 1, 2), (- 3, 0)
Find x if distance between points L(x, 7) and M(1, 15) is 10.
Find the distances between the following point.
A(a, 0), B(0, a)
Find the distance between the following pairs of points:
(–3, 6) and (2, –6)
Show that the points (a, a), (-a, -a) and `(-asqrt(3), asqrt(3))` are the vertices of an equilateral triangle.
If the length of the segment joining point L(x, 7) and point M(1, 15) is 10 cm, then the value of x is ______
Show that A(1, 2), (1, 6), C(1 + 2 `sqrt(3)`, 4) are vertices of a equilateral triangle
The point which divides the lines segment joining the points (7, -6) and (3, 4) in ratio 1 : 2 internally lies in the ______.
|
Case Study Trigonometry in the form of triangulation forms the basis of navigation, whether it is by land, sea or air. GPS a radio navigation system helps to locate our position on earth with the help of satellites. |
- Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower.
- After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(`sqrt(3)` - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower?
