Answer:
The coordinates of point B' are (-3, 4) ⇒ C
Step-by-step explanation:
If the point (x, y) reflected across the line x = a, then a is the x-coordinate of the midpoint of the segment joining the point and its image
∵ The coordinates of point B are (5, 4)
∴ x = 5 and y = 4
∵ The point B is reflected over the line x = 1
→ From the rule above
∴ a = 1
∵ The rule of the midpoint is M = ([tex]\frac{x1+x2}{2}[/tex] , [tex]\frac{y1+y2}{2}[/tex])
→ The point B is (x1, y1) and the point B' is (x2, y2)
∵ a is the x-coordinate of the midpoint of segment BB'
∴ a = [tex]\frac{x1+x2}{2}[/tex]
∵ x1 = 5 and x2 = x
→ Substitute the value of a, x1 and x2 in the rule above
∴ 1 = [tex]\frac{5+x}{2}[/tex]
→ Multiply both sides by 2
∵ 2 = 5 + x
→ Subtract 5 from both sides
∴ 2 - 5 = 5 - 5 + x
∴ -3 = x
∴ The x-coordinate of B' = -3
→ y-coordinate of B' = y-coordinate of B because the reflection across
x = a does not change the y-coordinate
∴ y-coordinate of B' = 4
∴ The coordinates of point B' are (-3, 4)
