Q1 of 10 Page 171

If two vertices of an equilateral triangle are (3, 0) and (6, 0). Find the third vertex.


Here given ΔABC,


B = (3,0) and C = (6,0)


We need to find the coordinates of point A.


AlSo, we know that ΔABC is equilateral.


So, we can say


l(AB) = l(AC) = l(BC)


l(AB) = (by distance formula)


=


=


l(AC) =


=


=


l(BC) = (by distance formula)


=


= = 3.


∴ we can write


⇒ = 3


Squaring both sides we get


= = 9


=


∴


∴ ……(1)


⇒ = 3


Squaring both sides we get


⇒ = 9


⇒ ……(2)


Substituting value of y2 in in (2) we get


⇒


⇒


∴


Putting value of in (1) we get


∴


⇒


⇒


∴ A() or A()


More from this chapter

All 10 →
2

Find the point on the y-axis that is equidistant from the points (5, –2) and (–3, 2).

 3

Three consecutive vertices of a parallelogram are (–2, –1) (1, 0) and (4, 3). Find the coordinates of the fourth vertex.

 4

If P(9a – 2, –b) divides the line segment joining A(3a + 1 ,–3) and B(8a ,5) in the ratio 3:1. Find the values of a & b.

 5

A line intersects the y–axis and x-axis at the points P and Q respectively. If (2 –5) is the midpoint of PQ, then find the coordinates of P and Q.