Question

12. The points A, B and C are (4,0), (2, 2) and (0, 6) respectively. AB produced cuts the y-axis at
P and CB produced cuts the x-axis at Q. Find the co-ordinates of the points P and Q. Find the
equation of the straight line joining the mid-points of AC and OB (where O is the origin), and
verify that this line passes through the mid-point of PQ.
[SC​

Answer 1

Step-by-step explanation:

The points A, B and C are (4,0), (2, 2) and (0, 6) respectively. AB produced cuts the y-axis at

P and CB produced cuts the x-axis at Q. Find the co-ordinates of the points P and Q. Find the

equation of the straight line joining the mid-points of AC and OB (where O is the origin), and

verify that this line passes through the mid-point of PQ.

[SC

Answer 2

for line AB (m) is =2-0/2-4=2/-2=2

since (x1, y1) =(4,0)

eq of line AB =y-y1=m(x-x1)

=y-0=-1(x-4)

=y+x=4 -eq(1)

for line BC (m) is =6-2/0-2=4/-2=-2

since (x1, y1) =(2,2)

eq of line AB =y-y1=m(x-x1)

=y-2=-2(x-2)

=2x+y=6 -eq(2)

given that AB cuts the y-axis at P. So the Abscissa at point P is 0.putting x=0 in ep (1). we get y=4.thus, the Co-ordinates of point P are (0, 4)

given that BC cuts the x-axis at Q. so the ordinates of point Q is (0) . putting y=0 in eq (2) . We get 2x=6

x=3 thus the Co-ordinates of point Q are (3, 0)

mid point of AC is (2, 3)

mid point of BC is (1, 1) By mid point formula

=(x1+x2/2, y1+y2/2)

eq of straight line joining the mid point of AC and BC is

y-y1=M(x-x1)

y-3 = (1-3)/(1-2) (x-2)

y-3 = 2(x-2)

therefore eq is 2x-y=1