Advertisements
Advertisements
प्रश्न
AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.
पर्याय
5
3
`sqrt(34)`
4
उत्तर
AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is `underlinebb(sqrt(34))`.
Explanation:
The three vertices are: A = (0, 3), O = (0, 0), B = (5, 0)
We know that, the diagonals of a rectangle are of equal length,
Length of the diagonal AB = Distance between the points A and B
Distance formula: d2 = (x2 – x1)2 + (y2 – y1)2
According to the question,
We have,
x1 = 0, x2 = 5
y1 = 3, y2 = 0
d2 = (5 – 0)2 + (0 – 3)2
d = `sqrt((5 - 0)^2 + (0 - 3)^2`
d = `sqrt(25 + 9)`
= `sqrt(34)`
Distance between A(0, 3) and B(5, 0) is `sqrt(34)`
Therefore, the length of its diagonal is `sqrt(34)`
APPEARS IN
संबंधित प्रश्न
If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also, find the length of AB.
Find the values of y for which the distance between the points P (2, -3) and Q (10, y) is 10 units.
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 :
(Sin θ - cosec θ , cos θ - cot θ) and (cos θ - cosec θ , -sin θ - cot θ)
Find the value of m if the distance between the points (m , -4) and (3 , 2) is 3`sqrt 5` units.
Find the relation between a and b if the point P(a ,b) is equidistant from A (6,-1) and B (5 , 8).
Find the coordinates of O, the centre passing through A( -2, -3), B(-1, 0) and C(7, 6). Also, find its radius.
Prove that the points P (0, -4), Q (6, 2), R (3, 5) and S (-3, -1) are the vertices of a rectangle PQRS.
If the distance between point L(x, 7) and point M(1, 15) is 10, then find the value of x
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.
