Question

Indicate the equation of the given line in standard form. Show all of your work for full credit. The line containing the diagonal, BD, of a square whose vertices are A(-3, 3), B(3, 3), C(3, -3), and D(-3, -3). Find two equations, one for each diagonal.

Answer 1

If we draw thm
the diagonals are lines AC and BD

so
slope=changey/changex
for 2 points the slope is (y2-y1)/(x2-x1)
find AC
AC is (-3,3) and (3,-3)
slope=(-3-3)/(3-(-3))=-6/(3+3)=-6/6=-1
slope is -1
and a point is (-3,3)
so
y=mx+b
m=slope
y=-1x+b
sub (-3,3)
3=-1(-3)+b
3=3+b
0=b
y=-1x is the equation for AC

for BD
(3,3) and (-3,-3)
slope is (-3-3)/(-3-3)=1
y=1x+b
find b
(3,3)
3=1(3)+b
3=3+b
0=b
y=x is equation of BD


the diagonals are y=-x and y=x
wait, standard form is ax+by=c
k
y=-x
x+y=0 is thefirst

y=x
x-y=0 is 2nd

the equations are
x+y=0 and x-y=0