Advertisements
Advertisements
Question
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.
Options
5 units
12 units
10 units
11 units
`7 + sqrt(5)` units
Advertisements
Solution
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.
RELATED QUESTIONS
Find the distance between two points
(i) P(–6, 7) and Q(–1, –5)
(ii) R(a + b, a – b) and S(a – b, –a – b)
(iii) `A(at_1^2,2at_1)" and " B(at_2^2,2at_2)`
Find the distance between the following pairs of points:
(2, 3), (4, 1)
An equilateral triangle has two vertices at the points (3, 4) and (−2, 3), find the coordinates of the third vertex.
If the point P(x, y ) is equidistant from the points A(5, 1) and B (1, 5), prove that x = y.
Find the distance of the following point from the origin :
(8 , 15)
Find the distance of a point (12 , 5) from another point on the line x = 0 whose ordinate is 9.
Find the coordinate of O , the centre of a circle passing through P (3 , 0), Q (2 , `sqrt 5`) and R (`-2 sqrt 2` , -1). Also find its radius.
A(-2, -3), B(-1, 0) and C(7, -6) are the vertices of a triangle. Find the circumcentre and the circumradius of the triangle.
ABC is an equilateral triangle . If the coordinates of A and B are (1 , 1) and (- 1 , -1) , find the coordinates of C.
A point P lies on the x-axis and another point Q lies on the y-axis.
Write the abscissa of point Q.
The centre of a circle is (2x - 1, 3x + 1). Find x if the circle passes through (-3, -1) and the length of its diameter is 20 unit.
Point P (2, -7) is the center of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of: AT
Calculate the distance between A (7, 3) and B on the x-axis, whose abscissa is 11.
Use distance formula to show that the points A(-1, 2), B(2, 5) and C(-5, -2) are collinear.
Show that the quadrilateral with vertices (3, 2), (0, 5), (- 3, 2) and (0, -1) is a square.
The distance between points P(–1, 1) and Q(5, –7) is ______
AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.
The equation of the perpendicular bisector of line segment joining points A(4,5) and B(-2,3) is ______.
What type of a quadrilateral do the points A(2, –2), B(7, 3), C(11, –1) and D(6, –6) taken in that order, form?
What is the distance of the point (– 5, 4) from the origin?
