Theorem: If two chords intersect within a circle, then the product of the lengths of the segments (parts) of one chord is equal to the product of the lengths of the segments of the other chord.
In your case,
If AE = 6, EB = 3, and DE = 2, then
Answer: correct choice is D.
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 = ( ,
)
→ 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 =
∵ x1 = 5 and x2 = x
→ Substitute the value of a, x1 and x2 in the rule above
∴ 1 =
→ 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)
