Posted by **JOJO** on Wednesday, June 5, 2013 at 11:01pm.

(a)Given the points P(3,5),Q(8,10)and R(8,0),find the equation of a line which is perpendicular to QR and passes through the mid point of QR.

(b)The line 2x+3y=2 and 7x-3y=10 intersect at A . Find the equation of the line which passes through A and is perpendicular to the line 3x-4y=7

- math -
**Reiny**, Thursday, June 6, 2013 at 7:48am
a) let M(8,5) be the midpoint of QR.

QR is a vertical line, so its slope is undefined.

A line perpendicular to QR must be a horizontal line

A horizontal line through M(8,5) is imply

y = 5

(Where does point P enter the picture ? )

b) Add the two equations ...

9x = 12

x = 12/9 = 4/3

sub into the first ...

8/3 + 3y = 2

3y = -2/3

y = -2/9

point A is (4/3 , -2/9)

The new line is to be perpendicular to

3x - 4y = 7

So it must have the form 4x + 3y = C

but (4/3 , -2/9) lies on it, so

16/3 - 6/9 = c

times 9 ....

48 - 6 = 9c

c = 14/3

we have 4x + 3y = 14/3

or

12x + 9y = 14

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