Answer:
(3,9)
Explanation:
The straight line which is perpendicular to the straight line y= -x is given by y=x +c {Since, the product of slopes of two mutually perpendicular straight line is -1}
Now, if this straight line passes through (-9, -3) point, then -3 =-9 +c, ⇒c =6.
Therefore, the straight line which is perpendicular to the line y=-x ....... (1) and passes through (-9,-3) point is y=x+6 ....... (2)
Now, solving (1) and (2) we get, 2y =6, ⇒ y=3 and from (1), x=-3
Therefore, equations (1) and (2) intersect at (-3, 3) point.
If (h,k) is the reflection point of (-9,-3) over the line y =-x, then (-3,3) must be the midpoint of (h,k) and (-9,-3) points.
Hence, (h-9)/2 =-3, ⇒h-9 =-6, ⇒h=3
and (k-3)/2 =3, ⇒ k-3 = 6, ⇒ k=9
Hence, (3,9) is the image point of (-9, -3) after reflection over the line y=-x. (Answer)