Points A and B have symmetry with respect to the
origin O. Find the coordinates of B if A is the point:
a) (3, 4) c) (a, 0)
b) (0, 2) d) (b, c)
for any point (a,b) , the image of (a,b) with symmetry with respect to the origin would yield the point (-a,-b)
so for (3,4) ----> (-3,-4)
I will let you do the others.
To find the coordinates of point B, which has symmetry with respect to the origin O given point A, we can use the fact that the origin is the midpoint between A and B.
a) (3, 4):
Since point A is (3, 4), the coordinates of B can be found by reflecting A over the origin. This means the x-coordinate of B will be the negative of A's x-coordinate, and the y-coordinate of B will be the negative of A's y-coordinate. So B will have coordinates (-3, -4).
b) (0, 2):
Since point A is (0, 2), reflecting A over the origin will give the same coordinates. So B will also be (0, 2).
c) (a, 0):
Since point A is (a, 0), reflecting A over the origin will give the same y-coordinate, but the x-coordinate will be the negative of A's x-coordinate. So B will have coordinates (-a, 0).
d) (b, c):
Since point A is (b, c), reflecting A over the origin will give the negative of A's x-coordinate and y-coordinate. So B will have coordinates (-b, -c).
To find the coordinates of point B given that points A and B have symmetry with respect to the origin O, we can use the concept of symmetry.
Symmetry with respect to the origin means that if you reflect a point over the origin, the x-coordinate and y-coordinate will change signs. In other words, for a point (x, y), its symmetric point with respect to the origin is (-x, -y).
Let's find the coordinates of B for each given point A:
a) Point A = (3, 4)
To find the coordinates of B, we need to change the signs of both x and y coordinates of A.
So, B = (-3, -4)
b) Point A = (0, 2)
Again, we need to change the signs of both x and y coordinates of A.
So, B = (0, -2)
c) Point A = (a, 0)
In this case, the y-coordinate of A is already 0, so the y-coordinate of B will remain 0.
To find the x-coordinate of B, we need to change the sign of the x-coordinate of A.
So, B = (-a, 0)
d) Point A = (b, c)
To find the coordinates of B, we need to change the signs of both x and y coordinates of A.
So, B = (-b, -c)
Therefore, the coordinates of point B for each given point A are:
a) B = (-3, -4)
b) B = (0, -2)
c) B = (-a, 0)
d) B = (-b, -c)