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
6 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.
APPEARS IN
RELATED QUESTIONS
If P and Q are two points whose coordinates are (at2 ,2at) and (a/t2 , 2a/t) respectively and S is the point (a, 0). Show that `\frac{1}{SP}+\frac{1}{SQ}` is independent of t.
If two vertices of an equilateral triangle be (0, 0), (3, `sqrt3`), find the third vertex using distance formula.
Prove that the points (–3, 0), (1, –3) and (4, 1) are the vertices of an isosceles right angled triangle. Find the area of this triangle
Find the distance between the following pairs of points:
(2, 3), (4, 1)
If Q (0, 1) is equidistant from P (5, –3) and R (x, 6), find the values of x. Also, find the distances QR and PR.
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 sin α, a cos α) and Q(a cos α, – a sin α)
Determine whether the points are collinear.
L(–2, 3), M(1, –3), N(5, 4)
Determine whether the point is collinear.
R(0, 3), D(2, 1), S(3, –1)
If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then ______.
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 :
(13 , 7) and (4 , -5)
Find the coordinate of O , the centre of a circle passing through A (8 , 12) , B (11 , 3), and C (0 , 14). Also , find its radius.
Find the co-ordinates of points on the x-axis which are at a distance of 17 units from the point (11, -8).
A point P lies on the x-axis and another point Q lies on the y-axis.
If the abscissa of point P is -12 and the ordinate of point Q is -16; calculate the length of line segment PQ.
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?
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.
If the point A(2, – 4) is equidistant from P(3, 8) and Q(–10, y), find the values of y. Also find distance PQ.
If (a, b) is the mid-point of the line segment joining the points A(10, –6) and B(k, 4) and a – 2b = 18, find the value of k and the distance AB.
Show that points A(–1, –1), B(0, 1), C(1, 3) are collinear.
