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