You start at (3, 0). You move right 1 unit and left 2 units. Where do you end?
1 answer:
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we know that
The rectangle has coordinates P (-1,2), Q(2,4), R(x,y) and S(3,-4)
using a graph tool
see the attached figure
Step 1
<u>Find the slope of the line PS</u>
the slope is equal to
m=(y2-y1)/(x2-x1)
mPS=(-4-2)/(3+1)=-6/4=-3/2
Step 2
<u>Find the equation of the line QR</u>
we know that
PS and QR are parallel lines
so
their slopes are the same
mQR=-3/2
with mQR and the point Q(2,4) find the equation of the line
y-y1=m*(x-x1)
y-4=(-3/2)*(x-2)
y=(-3/2)*x+3+4--------> y=7-(3/2)*x
Step 3
<u>Find the equation of the line SR</u>
we know that
SR and QR are perpendicular lines
so
the product of their slopes is equal to minus one
mSR*mQR=-1
mSR=2/3
with mSR and the point S(3,-4) find the equation of the line SR
y-y1=m*(x-x1)
y+4=(2/3)*(x-3)
y=(2/3)*x-2-4---------> y=-6+(2/3)*x
Step 4
Find the intersection of the lines QR and SR
we know that
the intersection of the lines QR and SR is the point R
y=7-(3/2)*x------> equation 1
y=-6+(2/3)*x------> equation 2
equate equation 1 and equation 2
7-(3/2)*x=-6+(2/3)*x
7+6=(2/3)*x+(3/2)*x
13=(2/3)*x+(3/2)*x
Multiply by 6 both sides
6*13=4*x+9*x
13*x=6*13
x=6
find the value of y
y=-6+(2/3)*x------> y=-6+(2/3)*6---------> y=-6+4
y=-2
therefore
<u>the answer is</u>
The coordinates of point R are (6,-2)
see the attached figure N 2
