Segment FG begins at point F(-2,4) and ends at point G(-2,-3). The segment is translated by the less than symbol x-3,y+2 greater than symbol and then reflected across the y-axis to form segment F'G'. How many units long is segment F'G'?
a. 0 b. 2 c. 3 d. 7
AAAAAAAhhHHHH I need a answer too
translations and reflections do not change distances. So, F'G' is the same length as FG.
I'm not sure what your saying Steve.
To find the length of segment F'G', we need to follow these steps:
1. Start with the original segment FG, with points F(-2,4) and G(-2,-3).
2. Apply the translation (x-3, y+2) to each point of the original segment FG. The translation moves each point three units to the right (x-3) and two units up (y+2). So, the new coordinates will be:
F'((-2 - 3), (4 + 2)) = F'(-5, 6)
G'((-2 - 3), (-3 + 2)) = G'(-5, -1)
3. Now, reflect the translated segment F'G' across the y-axis. This means we need to flip the x-coordinates of each point. The reflected coordinates are:
F'(-(-5), 6) = F'(5, 6)
G'(-(-5), -1) = G'(5, -1)
4. To find the length of segment F'G', we use the distance formula:
Length = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates of F'(5, 6) and G'(5, -1):
Length = √((5 - 5)^2 + (-1 - 6)^2)
= √(0^2 + (-7)^2)
= √(0 + 49)
= √49
= 7
Therefore, the length of segment F'G' is 7 units. So, the correct answer is d. 7.