Advertisements
Advertisements
Question
Prove that the points (1 ,1),(-4 , 4) and (4 , 6) are the certices of an isosceles triangle.
Solution
PQ = `sqrt ((1 + 4)^2 + (1 - 4)^2) = sqrt (25 + 9) = sqrt 34` units
QR = `sqrt ((-4-4)^2 + (4 - 6)^2) = sqrt (64 + 4) sqrt 68` units
PR = `sqrt ((4 - 1)^2 + (6 - 1)^2) = sqrt (9 + 25) = sqrt 34` units
∵ PQ = QR
∴ P,Q and R are the vertices of an isosceles triangle.
APPEARS IN
RELATED QUESTIONS
Find the coordinates of the centre of the circle passing through the points (0, 0), (–2, 1) and (–3, 2). Also, find its radius.
Find the co-ordinates of points of trisection of the line segment joining the point (6, –9) and the origin.
Using the distance formula, show that the given points are collinear:
(-1, -1), (2, 3) and (8, 11)
Find the distance between the following pair of point.
P(–5, 7), Q(–1, 3)
Determine whether the points are collinear.
A(1, −3), B(2, −5), C(−4, 7)
Show that the points A(1, 2), B(1, 6), C(1 + 2`sqrt3`, 4) are vertices of an equilateral triangle.
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.
x (1,2),Y (3, -4) and z (5,-6) are the vertices of a triangle . Find the circumcentre and the circumradius of the triangle.
Find the distance between the following pairs of points:
`(3/5,2) and (-(1)/(5),1(2)/(5))`
Calculate the distance between the points P (2, 2) and Q (5, 4) correct to three significant figures.
