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A square ABCD and a rectangle PQRS lie in the xy-plane. Coordinates of
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07 Sep 2023, 01:29
07 Sep 2023, 01:29
1
Expert Reply
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Question Stats:
46% (02:26) correct
53% (02:29) wrong based on 13 sessions
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A square ABCD and a rectangle PQRS lie in the xy-plane. Coordinates of point A and C respectively are (3, 5) and (0, 2) where as the coordinates of point P and R respectively are (3, –4) and (4, 6).
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Quantity A |
Quantity B |
Area of square ABCD |
Area of rectangle PQRS |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
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Re: A square ABCD and a rectangle PQRS lie in the xy-plane. Coordinates of
[#permalink]
24 Sep 2023, 09:10
24 Sep 2023, 09:10
Answer should be B?
Re: A square ABCD and a rectangle PQRS lie in the xy-plane. Coordinates of
[#permalink]
24 Sep 2023, 12:35
24 Sep 2023, 12:35
Expert Reply
OE
For Square ABCD, Coordinates of A and C are given as (3, 5) and (0, 2) respectively.
So, we can find the length of diagonal for square ABCD. AC = √(0 − 3)^2 + (2 − 5)^2 = 3√2
If we have a length of diagonal AC, we can find out the area of the square.
Area of square = 1/2 (𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑑𝑖𝑎𝑔𝑜𝑛𝑎𝑙𝑠)
Area of Square ABCD = 1/2 × 3√2 × 3√2 = 9 Square units
For rectangle PQRS, as coordinates of P and R are given as (3, - 4) and (4,6), we can find out the length of diagonal PR. PR = √(4 − 3)^2 + (6 + 4)^2 = √101
Area of the rectangle is maximum, when it is a square.
So maximum area of Rectangle PQRS = 1/2× √101 × √101 = 101/2 square units.
Minimum area of Rectangle PQRS could go close to Zero as well.
Area of rectangle PQRS varies from a ‘value close to zero’ to 101/2 square units.
As it varies, we cannot compare the area of Rectangle PQRS to the area of Square
ABCD.
Ans. (D)
For Square ABCD, Coordinates of A and C are given as (3, 5) and (0, 2) respectively.
So, we can find the length of diagonal for square ABCD. AC = √(0 − 3)^2 + (2 − 5)^2 = 3√2
If we have a length of diagonal AC, we can find out the area of the square.
Area of square = 1/2 (𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑑𝑖𝑎𝑔𝑜𝑛𝑎𝑙𝑠)
Area of Square ABCD = 1/2 × 3√2 × 3√2 = 9 Square units
For rectangle PQRS, as coordinates of P and R are given as (3, - 4) and (4,6), we can find out the length of diagonal PR. PR = √(4 − 3)^2 + (6 + 4)^2 = √101
Area of the rectangle is maximum, when it is a square.
So maximum area of Rectangle PQRS = 1/2× √101 × √101 = 101/2 square units.
Minimum area of Rectangle PQRS could go close to Zero as well.
Area of rectangle PQRS varies from a ‘value close to zero’ to 101/2 square units.
As it varies, we cannot compare the area of Rectangle PQRS to the area of Square
ABCD.
Ans. (D)
