The coordinates of two vertices of square ABCD are A(2,1) and B(4,4). Determine the slope of side BC. Does this question require the use of point-slope form or something? And perpendicular lines?...

The coordinates of two vertices of square ABCD are A(2,1) and B(4,4). Determine the slope of side BC.

Does this question require the use of point-slope form or something? And perpendicular lines? Please explain in detail that is easy for me to understand.

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ishpiro's profile pic

ishpiro | College Teacher | (Level 1) Educator

Posted on

The slope of the line connecting two points with given coordinates can be found using the slope formula:

`m=(y_2 - y_1)/(x_2 - x_1)`

So the slope of AB will be

`m_(AB) = (y_B-y_A)/(x_B - x_A) = (4-1)/(4-2) = 3/2`

Since AB and BC are adjacent sides of a square, they are perpendicular to each other. The slopes of perpendicular lines are negative reciprocals, that is, they obey the relationship

`m_(AB)*m_(BC) = -1`

From here, `m_(BC)= -1/m_(AB) = -1/(3/2) = -2/3` ` `

So the slope of BC is -2/3.

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kspcr111's profile picture

kspcr111 | In Training Educator

Posted on

This is easy 

the slope of AB is = `(y2 -y1)/(x2-x1)` = `(4-1)/(4-2)` = `3/2`

As in the square all sides ae perpendicular to each other then

AB is perpendicular to BC so,

(slope of AB)*(slope of BC)= -1

so,

slope of BC= -1/(slope of AB)

                = -1/(3/2)

                 = `(-2)/3`

              :)

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Nolan McShea | Student, Grade 11 | (Level 2) Honors

Posted on

Wow, that was simpler than I thought. I nearly forgot what the question was asking and thought that it was asking for the coordinates of one of the points.

Thanks!

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