SOLUTION: Dear math tutor, A(7,2) and C(1,4) are two vertices of a square ABCD. Find the equation of the diagonal BD. Find the coordinates of B and D. with gratitude, nats

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Question 870669: Dear math tutor,
A(7,2) and C(1,4) are two vertices of a square ABCD. Find the equation of the diagonal BD. Find the coordinates of B and D.
with gratitude,
nats
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!

Find the slope of the line connecting A and C.

Diagonal BD is perpendicular to diagonal AC so their slopes are negative reciprocals of each other.


Diagonal BD also goes through the midpoint of AC.


Use this point to find the line, BC,


.
.
.


.
.
The distance from the midpoint to points B and D is the same as the distance from the midpoint to A and C.



The distance from the midpoint to B and D is,

But you also know that B and D lie on the line
So substituting.






Two solutions:


Then


and


Then,


B and D are (3,0) and (5,6)
.
.
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