Maths-
General
Easy
Question
𝐴𝑃 is perpendicular bisector of 𝐵𝐶.
1. What segment lengths are equal? Explain your reasoning.
2. Find AB.
3. Explain why D is on 𝐴𝑃.
Hint:
- Perpendicular bisector theorem
- According to perpendicular bisector theorem, in the triangle, any point on perpendicular bisector is at equal distance from both end points of the line segment on which it is drawn.
The correct answer is: 1. equal segments AB = BC, BD = DC and BP = PC 2. AB = 4 units. 3.Yes, D lie on AP.
Answer:
- Step by step explanation:
- Given:
AB = 6x - 5.
AC = 4x + 1.
BD = 13
DC = 13
AP is perpendicular bisector at BC.
- Step 1:
In 
AP is perpendicular bisector.
Therefore, points on AP are equidistant from B and C
So,
AB = AC
6x – 5 = 4x + 1
6x – 4x = 5 + 1
2x = 6
x = 1.5
AB = 6x – 5
AB = 6(1.5) – 5
AB = 9 – 5
AB = 4
- Step 2:
- Given:
BD = 13
DC = 13
Therefore, 
Also, BP = PC
DP is perpendicular bisector on BC from D.
Also,
As point D is equidistant from B and C
Therefore, D lies on DP
- Final Answer:
- equal segments AB = BC, BD = DC and BP = PC
- AB = 4 units.
- Yes, D lie on AP.
- Given:
AP is perpendicular bisector at BC.
DP is perpendicular bisector on BC from D.
Also,
As point D is equidistant from B and C
Therefore, D lies on DP
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37. In an academic contest correct answers earn 12 points and incorrect answers lose 5
points. In the final round, school A starts with 165 points and gives the same number
of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.
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