The image of (a,b) with respect to
x+y=0
Answers
Answer:
Step-by-step explanation:
Let line AB be x+3y=7 and point P be (3,8).
Let Q(h,k) be the image of point P(3,8) in the line x+3y=7.
Since line AB is a mirror,
1) Point P and Q are at equal distance from line AB, i.e., PR=QR, i.e., R is the mid-point of PQ.
2) Image is formed perpendicular to mirror i.e., line PQ is perpendicular to line AB.
Since R is the midpoint of PQ.
Mid point of PQ joining (3,8) and (h,k) is (
2
h+3
,
2
k+8
)
Coordinate of point R = (
2
h+3
,
2
k+8
)
Since point R lies on the line AB.
Therefore,
(
2
3+h
)+3(
2
8+k
)=7
h+3k=−13 ....(1)
Also, PQ is perpendicular to AB.
Therefore,
Slope of PQ × Slope of AB=−1
Since, slope of AB= −
3
1
Therefore, slope of PQ= 3
Now, PQ is line joining P(3,8) and Q(h,k).
Slope of PQ = 3=
h−3
k−8
3h−k=1 ........(2)
Solving equation 1 and 2, we get,
h=−1 and k=−4
Hence, image is Q(−1,−4).