Question

The endpoints of a side of rectangle ABCD in the coordinate plane are at A(1, 7) and

Answer 1

Answer:

  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.