Advertisements
Advertisements
Question
Show that the following points taken in order to form an equilateral triangle
`"A"(2, 2), "B"(-2, -2), "C"(-2sqrt(3), 2sqrt(3))`
Advertisements
Solution
Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
AB = `sqrt((-2 - 2)^2 + (-2 - 2)^2`
= `sqrt((-4)^2 + (-4)^2`
= `sqrt(16 + 16)`
= `sqrt(32)`
BC = `sqrt((-2sqrt(3) + 2)^2 + (2sqrt(3) + 2)^2`
= `sqrt(12 + 4 - 8sqrt(3) + 12 + 4 + 8sqrt(3))`
= `sqrt(16 + 16)`
= `sqrt(32)`
AC = `sqrt((-2sqrt(3) - 2)^2 + (2sqrt(3) - 2)^2`
= `sqrt((2sqrt(3) + 2)^2 + (2sqrt(3) - 2)^2`
= `sqrt(12 + 4 + 8sqrt(3) + 12 + 4 - 8sqrt(3))`
= `sqrt(16 + 16)`
= `sqrt(32)`
AB = BC = AC ...(Three sides are equal)
∴ ABC is an equilateral triangle.
APPEARS IN
RELATED QUESTIONS
Find the distance with the help of the number line given below.
d (Q, B)
If the co-ordinate of A is x and that of B is y, find d(A, B).
x = - 3, y = 7
Sketch proper figure and write the answer of the following question.
If R-S-T and l(ST) = 3.7, l(RS) = 2.5, then l(RT) = ?
On a number line, co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statement is true or false.
d(P, Q) + d(Q, R) = d(P, R)
Co-ordinates of the pair of points are given below. Hence find the distance between the pair.
- 4, 5
Co-ordinate of point P on a number line is - 7. Find the co-ordinates of points on the number line which are at a distance of 8 units from point P.
Co-ordinate of point A on a number line is 1. What are the co-ordinates of points on the number line which are at a distance of 7 units from A?
Find the distance between the following pair of points
(3, 4) and (−7, 2)
Show that the following points taken in order to form an isosceles triangle
A(5, 4), B(2, 0), C(−2, 3)
Show that the following points taken in order to form the vertices of a parallelogram
A(−3, 1), B(−6, −7), C(3, −9) and D(6, −1)
