Question

The base of an equilateral triangle is x + y - 2 = 0 and the opposite vertex is (2, -1). Find the equation of the remaining sides.

Answer 1

Answer:

$y=0.268x-1.536$

$y=3.732x-8.464$

Step-by-step explanation:

The base of an equilateral triangle is x + y - 2 = 0 and opposite vertex is (2,-1)

First we write the equation in slope intercept form: y=-x+2

Slope of base, m=-1

We are given an equilateral triangle. The each angle of triangle is 60°

Let slope of line AB is a

Slope of line line base BC=-1

Formula:

$\tan\theta=|\dfrac{m_1-m_2}{1+m_1m_2}|$

$\tan 60^\circ=|\dfrac{-1-a}{1-a}|$

Using calculator to solve for a

$a=3.732, 0.268$

Slope of another side of two line, 3.732 and 0.268

Slope of line AB, 0.268 and passing point (2,-1)

Using point slope form, Equation of line AB

$y+1=0.268(x-2)$

Equation of line AB, $y=0.268x-1.536$

Slope of line AC, 3.732 and passing point (2,-1)

Using point slope form, Equation of line AB

$y+1=3.732(x-2)$

Equation of line AC, $y=3.732x-8.464$

Hence, The equation of remaining side $y=0.268x-1.536$ and $y=3.732x-8.464$

Answer 2

Step-by-step explanation:

x+y= 2 ....... i)

the point of vertex (2, -1)

putting above values in equation i)

2-1 is not equal to 2

(2, -1) does not satisfy the equation i)

rest you can see in the given above attachment.

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