The endpoints of a side of rectangle abcd in the coordinate plane are at a(1, 7) and
b(4, 1). find the equation of the line that contains the given segment.

the line segment is bc.

the equation is y =

  y = 1/2x -1

Step-by-step explanation:

The slope of AB is ...

  (y2 -y1)/(x2 -x1) = (1 -7)/(4 -1) = -6/3 = -2

Segment BC will be perpendicular to AB, so will have a slope that is the negative reciprocal of this:

  slope of BC = -1/(-2) = 1/2

The line containing BC must go through point B, so we can use a point-slope form of the equation for a line:

  y = m(x -h) +k . . . . for a line with slope m through point (h, k)

Point B is (4, 1) and our slope is 1/2, so the line's equation can be written ...

  y = (1/2)(x -4) +1

  y = 1/2x -2 +1 . . . . eliminate parentheses

  y = 1/2x -1 . . . . . . . collect terms. This is the equation.

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The attachment shows segment AB and a perpendicular line through B. You will note that it has y-intercept -1 and slope 1/2, as above.

a

step-by-step explanation:

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