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2. In the xy-plane above, ABCD is a square and point E is the center of the square. The coordinates of points C and E are (7,2) and (1,0), respectively. Write an equation of the line that passes through points A, E, and C. 6 2 C X A D

2 In The Xyplane Above ABCD Is A Square And Point E Is The Center Of The Square The Coordinates Of Points C And E Are 72 And 10 Respectively Write An Equation O class=

Answer :

Given ABCD is a square

The coordinates of point C = ( 7 , 2 )

The coordinates of point E = (1 , 0 )

We need to find the equation of the line passing through the points A , E and C

The general equation of the required line is:

[tex]y=mx+b[/tex]

Where m is the slope and b is a constant

the slope = Rise/Run

Rise = 2 - 0 = 2

Run = 7 - 1 = 6

Slope = 2/6 = 1/3

so,

[tex]y=\frac{1}{3}x+b[/tex]

using the point E = (1 , 0 ) to find the value of b

when x = 1 , y = 0

[tex]\begin{gathered} 0=\frac{1}{3}\cdot1+b \\ b=-\frac{1}{3} \end{gathered}[/tex]

So, the equation of the line is :

[tex]y=\frac{1}{3}x-\frac{1}{3}[/tex]

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