Answer:
To reflect a point over another point, we can use the following steps:
1. Find the vector from the point of reflection (in this case, (-1, -5)) to the point being reflected (A(-5, -4)). This vector is (-5, -4) - (-1, -5) = (-4, 1).
2. Multiply the vector found in step 1 by 2. This gives us the vector (-8, 2).
3. Add the vector found in step 2 to the point of reflection. This gives us (-1, -5) + (-8, 2) = (-9, -3).
Therefore, the coordinates of point B, the image of A after reflection, are (-9, -3).
Answer:
B = (3, -6)
Explanation:
If point A(-5 -4) is reflected over point (-1, -5) then (-1, -5) is the midpoint of these two points. Let point B be (x, y).
Use midpoint formula:
[tex]\sf (x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]
put in the values:
[tex]\sf (-1, -5) = (\dfrac{x-5}{2}, \dfrac{y-4}{2})[/tex]
solve x and y separately:
[tex]\sf \dfrac{x-5}{2}=-1[/tex]
[tex]\sf x-5=-2[/tex]
[tex]\sf x=-2+5 = 3[/tex]
[tex]\sf \dfrac{y-4}{2} = -5[/tex]
[tex]\sf y-4= -10[/tex]
[tex]\sf y= -6[/tex]
So the point B is (3, -6) as figured out in the above solution.
