Advertisements
Advertisements
प्रश्न
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.
पर्याय
5 units
12 units
10 units
11 units
`7 + sqrt(5)` units
Advertisements
उत्तर
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is 12 units.
Explanation:
The vertices of a triangle are (0, 4), (0, 0) and (3, 0).
Now, perimeter of ΔAOB = Sum of the length of all its sides
= Distance between (OA + OB + AB)
Distance between the points (x1, y1) and (x2, y2) is given by,
d = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
To find:
Distance between A(0, 4) and O(0, 0) + Distance between O(0, 0) and B(3, 0) + Distance between A(0, 4) and B(3, 0)
= `sqrt((0 - 0)^2 + (0 - 4)^2) + sqrt((3 - 0)^2 + (0 - 0)^2) + sqrt((3 - 0)^2 + (0 - 4)^2)`
= `sqrt(0 + 16) + sqrt(9 + 0) + sqrt((3)^2 + (4)^2`
= `4 + 3 + sqrt(9 + 16)`
= `7 + sqrt(25)`
= 7 + 5
= 12
Therefore, the required perimeter of the triangle is 12.
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.
If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.
If P (2, – 1), Q(3, 4), R(–2, 3) and S(–3, –2) be four points in a plane, show that PQRS is a rhombus but not a square. Find the area of the rhombus
Find the distance between the following pairs of points:
(a, b), (−a, −b)
Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.
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 points:
(-6, 7) and (-1, -5)
Find the distance between the following pair of points:
(a+b, b+c) and (a-b, c-b)
If the points (2, 1) and (1, -2) are equidistant from the point (x, y), show that x + 3y = 0.
Find the distance of the following points from the origin:
(i) A(5,- 12)
If the point A(x,2) is equidistant form the points B(8,-2) and C(2,-2) , find the value of x. Also, find the value of x . Also, find the length of AB.
Find the distance between the following pair of points.
L(5, –8), M(–7, –3)
Find the distance of the following point from the origin :
(13 , 0)
Find the distance between the following point :
(Sin θ - cosec θ , cos θ - cot θ) and (cos θ - cosec θ , -sin θ - cot θ)
A(2, 5), B(-2, 4) and C(-2, 6) are the vertices of a triangle ABC. Prove that ABC is an isosceles triangle.
Find the point on y-axis whose distances from the points A (6, 7) and B (4, -3) are in the ratio 1: 2.
Find the distance of the following points from origin.
(a cos θ, a sin θ).
The distance between points P(–1, 1) and Q(5, –7) is ______
Find distance between point Q(3, – 7) and point R(3, 3)
Solution: Suppose Q(x1, y1) and point R(x2, y2)
x1 = 3, y1 = – 7 and x2 = 3, y2 = 3
Using distance formula,
d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `sqrt(square - 100)`
∴ d(Q, R) = `sqrt(square)`
∴ d(Q, R) = `square`
Find distance between points P(– 5, – 7) and Q(0, 3).
By distance formula,
PQ = `sqrt(square + (y_2 - y_1)^2`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(125)`
= `5sqrt(5)`
