Question

ABC is an equilateral triangle with coordinates of b and c as (1,0)and (5,0) respectively. find the coordinates of a.

Answer 1

★ coordinates of A are (3,2√3)

★ refer to attachment for more details

Answer 2

Answer:

$coordinates \: of \:A =( 3,2\sqrt{3})$

$coordinates \: of \:A' =( 3,-2\sqrt{3})$

Step-by-step explanation:

Given ,ABC is an equilateral triangle with coordinates of b and c as (1,0)and (5,0) respectively,

$i) B(1,0) \:and \: C(5,0)\\x_{1}=1, \:y_{1}=0;\\x_{2}=5, \:y_{2}=0;\\</p><p>Distance \:BC = | x_{2}-x_{1} |\\=| 5-1|\\=4 \:--(1)$

$ii)!Altitude (AD) = \frac{\sqrt{3}}{2}\times BC\\=\frac{\sqrt{3}}{2}\times 4\\=2\sqrt{3}\:---(2)$

$Now,\\coordinates \: of \:A =( 3,2\sqrt{3})$

$coordinates \: of \:A' =( 3,-2\sqrt{3})$

Therefore,

$coordinates \: of \:A =( 3,2\sqrt{3})$

$coordinates \: of \:A' =( 3,-2\sqrt{3})$

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