Question

(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

Answer 1

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