Answer:
y=-3x+15
Step-by-step explanation:
the midpoint of UV (using the midpoint formula) is (3,6)
the slope of UV= 4/12= (1/3)
perpendicular slope is -3
now find line with slope -3 passing (3,6)
y-6=-3(x-3)
y=-3x+15
The equation of the perpendicular bisector of the segment with endpoints U(-3,4) and V(9,8) is : y=-3x+15
We have the endpoints U(-3,4) and V(9,8)
The midpoint of UV is
[tex]=(\frac{(-3+9)}{2} ,\frac{(4+8)}{2})\\=(3,6)[/tex]
Now, the slope of line UV
[tex]= \frac{4}{12} \\=\frac{1}{3}[/tex]
The perpendicular slope will be -3
Now, equation of the tangent line with slope -3 passing through point (3,6) is:
y-6=-3(x-3)
y=-3x+15
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