Advertisements
Advertisements
Question
Show that the following points taken in order to form an equilateral triangle
`"A"(sqrt(3), 2), "B"(0, 1), "C"(0, 3)`
Advertisements
Solution
Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
AB = `sqrt((0 - sqrt(3))^2 + (1 - 2)^2`
= `sqrt((- sqrt(3))^2 + (-1)^2`
= `sqrt(3 + 1)`
= `sqrt(4)`
= 2
BC = `sqrt((0 - 0)^2 + (3 - 1)^2`
= `sqrt(0^2 + 2^2)`
= `sqrt(4)`
= 2
AC = `sqrt((0 - sqrt(3))^2 + (3 - 2)^2`
= `sqrt((- sqrt(3))^2 + 1^2)`
= `sqrt(3 + 1)`
= `sqrt(4)`
= 2
AB = BC = AC ...(Three sides are equal)
∴ ABC is an equilateral triangle.
APPEARS IN
RELATED QUESTIONS
If P - Q - R and d(P, Q) = 2, d(P, R) = 10, then find d(Q, R).
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, R) + d(R, Q) = d(P, Q)
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.
Determine whether the given set of points are collinear or not
(7, −2), (5, 1), (3, 4)
Verify that the following points taken in order to form the vertices of a rhombus
A(3, −2), B(7, 6), C(−1, 2) and D(−5, −6)
Let A(2, 3) and B(2, −4) be two points. If P lies on the x-axis, such that AP = `3/7` AB, find the coordinates of P.
The point whose ordinate is 4 and which lies on the y-axis is _______________
If the points A(2, 0), B(– 6, 0), C(3, a – 3) lie on the x-axis then the value of a is _____
If (x + 2, 4) = (5, y – 2), then the coordinates (x, y) are _____
Find the distance with the help of the number line given below.
d(P, J)
