Math CentralQuandaries & Queries


Question from Mitchell, a student:

The perimeter of rectangle ABCD (represented on a Cartesian plane) is 52cm.
The equation associated with segment AD is 3x+4y-60=0
Point C is at (18, 14).
What is the length of segment AD?


I redrew the diagram that you sent.


Write the equation of the line through AD, 3x + 4y - 60 = 0, in the form y = mx + b. I got

y = -3/4 x + 15/2.               (*)

Thus the slope of this line is -3/4. Since ABCD is a rectangle CD is perpendicular to AD and thus its slope is the negative reciprocal of -3/4, that is 4/3.

Write the equation of the line through (18, 14) with slope 4/3. Solve this equation with equation (*) to find the coordinates of D. Find the distance between C and D. Since you know the perimeter is 52 cm you can now find the length of the segment AD.


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