find the image of the point (-3,2) about the line 2x+ y - 9 =0
Answers
Answer:
ANSWER
Let image of P is Q
∴ PM = MQ & PQ ⊥ AB
Let Q is (h, k)
∴ M is (
2
h−1
,
2
k+2
)
It lies on 2x - 3y + 4 = 0
∴2(
2
h−1
)−3(
2
k+2
)+4=0
or 2h - 3k = 0 .......(i)
slope of PQ =
h+1
k−2
PQ⊥AB
∴
h+1
k−2
×
3
2
=−1
⇒ 3h + 2k - 1 = 0 ........(ii)
solving (i) & (ii) we get h =
13
3
, k =
13
2
∴ Image of P(-1, 2) is Q(
13
3
,
13
2
)ANSWER
Let image of P is Q
∴ PM = MQ & PQ ⊥ AB
Let Q is (h, k)
∴ M is (
2
h−1
,
2
k+2
)
It lies on 2x - 3y + 4 = 0
∴2(
2
h−1
)−3(
2
k+2
)+4=0
or 2h - 3k = 0 .......(i)
slope of PQ =
h+1
k−2
PQ⊥AB
∴
h+1
k−2
×
3
2
=−1
⇒ 3h + 2k - 1 = 0 ........(ii)
solving (i) & (ii) we get h =
13
3
, k =
13
2
∴ Image of P(-1, 2) is Q(
13
3
,
13
2
)
solution
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