Maths-
General
Easy
Question
Determine whether 𝐴𝐵 and 𝐶𝐷 are congruent. 𝐴 ≡ (3,4), 𝐵 ≡ (−2,4), 𝐶 ≡ (1, −3), 𝐷 ≡ (1,2).
Hint:
Distance between two points having coordinates (x
1
, y
1
) and (x
2
, y
2
) is given by formula:
- Distance
- AB and CD are congruent when AB = CD
- Distance between two points having coordinates (x
- , y
- ) and (x
- , y
- Distance
- AB and CD are congruent when AB = CD
The correct answer is: AB and CD are congruent.
Step by step explanation:
- Given:
𝐴 ≡ (3,4), 𝐵 ≡ (−2,4), 𝐶 ≡ (1, −3), 𝐷 ≡ (1,2).
- Step 1:
- Find AB:
Distance =
AB =
AB =
AB =
AB =
AB = 5
AB = 5 units.
- Step 2:
- Find CD:
Distance =
CD =
CD =
CD =
CD =
CD = 5
CD = 5 units.
It is clear that,
AB = CD
Hence, AB and CD are congruent.
- Given:
AB = 5 units.
CD = 5 units.
It is clear that,
AB = CD
Hence, AB and CD are congruent.
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