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1)

Let line  be the graph of . Line  is perpendicular to line  and passes through the point . If line  is the graph of the equation , then find .

2)

The perpendicular bisector of the line segment  is the line that passes through the midpoint of  and is perpendicular to .
Find the equation of the perpendicular bisector of the line segment joining the points  and  Enter your answer in the form "."

Nov 10, 2017

#1
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IDK how to solve this so yeah, have fun.

Nov 10, 2017
#2
+7350
+2

1)   First we need to find the slope of  l1 . Let's get its equation into slope-intercept form.

5x + 8y  =  -9          Subtract  5x  from both sides of the equation.

8y  =  -5x - 9           Divide through by  8 .

y  =  -$$\frac58$$x - $$\frac98$$

Now we can see that the slope of  l1  =  -$$\frac58$$  .

Line  l2  is perpendicular to  l1  , so the slope of  l2  =  +$$\frac85$$  .

Line  l2  has a slope of  $$\frac85$$  and passes through the point  (10, 10) .

So.... in point - slope form, the equation of  l2  is

y - 10  =  $$\frac85$$(x - 10)             We want this in the form  y = mx + b  . Distribute the  $$\frac85$$ .

y - 10  =  $$\frac85$$x - $$\frac85$$(10)

y - 10  =  $$\frac85$$x - 16               Add  10  to both sides.

y  =  $$\frac85$$x - 6

Now the equation for  l2  is in the form  y = mx + b  , where  m = $$\frac85$$  and  b = -6 .

We can look at a graph to verify that  l1  and  l2  are perpendicular, and  l2  passes through (10, 10) .

m + b   =  $$\frac85$$ + -6   =   -4.4

Nov 10, 2017
edited by hectictar  Nov 10, 2017
#3
+7350
+2

2)

The midpoint of  (1, 2)  and  (7, 4)  $$=\,(\frac{1+7}{2},\frac{2+4}{2}) \,=\,(\frac82,\frac62)$$  =  (4, 3)

The slope between  (1, 2)  and  (7, 4)  $$=\,\frac{4-2}{7-1}\,=\,\frac26\,=\,\frac13$$

So the slope of the perpendicular bisector   =   -$$\frac31$$   =   -3

We want an equation of a line that passes through  (4, 3)  with a slope of  -3 .

In point-slope form, that is

y - 3  =  -3(x - 4)         This is the equation of the line. We need it in  y = mx + b  form.

Distribute the  -3 .

y - 3  =  -3x + 12