Advertisements
Advertisements
Question
Write the perimeter of the triangle formed by the points O (0, 0), A (a, 0) and B (0, b).
Advertisements
Solution
The distance d between two points `(x_1 , y_1) ` and `(x_2 , y_2)` is given by the formula
`d = sqrt((x_1 - x_2)^2 + (y_1 - y_2)^2)`
The perimeter of a triangle is the sum of lengths of its sides.
The three vertices of the given triangle are O(0, 0), A(a, 0) and B(0, b).
Let us now find the lengths of the sides of the triangle.
`OA = sqrt((0 - a)^2 + (0-0)^2)`
`= sqrt(a^2)`
`OA = a`
`AB = sqrt((a - 0)^2 + (0-b)^2)`
`AB = sqrt(a^2 + b^2)`
`OB = sqrt((0 - 0)62 + (0 - b)^2)`
`= sqrt(b^2)`
`OB = b `
The perimeter ‘P’ of the triangle is thus,
p = OA + AB + OB
`= a + sqrt(a^2 + b^2) + b`
`P = a + b + sqrt(a^2 + b^2)`
Thus the perimeter of the triangle with the given vertices is `a + b + sqrt(a^2 + b^2)` .
RELATED QUESTIONS
Let ABCD be a square of side 2a. Find the coordinates of the vertices of this square when The centre of the square is at the origin and coordinate axes are parallel to the sides AB and AD respectively.
Find the coordinates of the circumcentre of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also, find its circumradius.
Find a point on the x-axis which is equidistant from the points (7, 6) and (−3, 4).
Find the equation of the perpendicular bisector of the line segment joining points (7, 1) and (3,5).
Prove that the points (3, 0), (4, 5), (-1, 4) and (-2, -1), taken in order, form a rhombus.
Also, find its area.
In the seating arrangement of desks in a classroom three students Rohini, Sandhya and Bina are seated at A(3, 1), B(6, 4), and C(8, 6). Do you think they are seated in a line?
Prove that the points (3, -2), (4, 0), (6, -3) and (5, -5) are the vertices of a parallelogram.
Show hat A(1,2), B(4,3),C(6,6) and D(3,5) are the vertices of a parallelogram. Show that ABCD is not rectangle.
The line segment joining the points A(3,−4) and B(1,2) is trisected at the points P(p,−2) and Q `(5/3,q)`. Find the values of p and q.
`"Find the ratio in which the poin "p (3/4 , 5/12) " divides the line segment joining the points "A (1/2,3/2) and B (2,-5).`
Find the ratio in which the pint (-3, k) divide the join of A(-5, -4) and B(-2, 3),Also, find the value of k.
If the points P (a,-11) , Q (5,b) ,R (2,15) and S (1,1). are the vertices of a parallelogram PQRS, find the values of a and b.
Find the value of k if points A(k, 3), B(6, −2) and C(−3, 4) are collinear.
What is the distance between the points (5 sin 60°, 0) and (0, 5 sin 30°)?
If the mid-point of the segment joining A (x, y + 1) and B (x + 1, y + 2) is C \[\left( \frac{3}{2}, \frac{5}{2} \right)\] , find x, y.
If P (x, 6) is the mid-point of the line segment joining A (6, 5) and B (4, y), find y.
If the distance between the points (4, p) and (1, 0) is 5, then p is equal to ______.
The distance of the point P(2, 3) from the x-axis is ______.
Statement A (Assertion): If the coordinates of the mid-points of the sides AB and AC of ∆ABC are D(3, 5) and E(–3, –3) respectively, then BC = 20 units.
Statement R (Reason): The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of it.
Assertion (A): The point (0, 4) lies on y-axis.
Reason (R): The x-coordinate of a point on y-axis is zero.
