If points X and Y are two distinct points in the coordinate plane, whi

Question

If points X and Y are two distinct points in the coordinate plane, which of the following can have more than one possible value?

A. The circumference of a circle with diameter XY. 
B. The area of a square with diagonal XY. 
C. The perimeter of a right isosceles triangle with a leg XY. 
D. The area of a circle with chord XY. 
E. The area of an equilateral triangle with base XY.

souvonik2k · Answer

IMO C.
All other options will have distinct values.

Sorrow · Answer

IMO D since there are an infinite number of chords that can be created in a circle.
In a right isosceles triangle if length of one of the legs is x then the other leg will also be x and hypotenuse will be \sqrt{2x^2}.
Hence the perimeter will always be 2x+ \sqrt{2x^2}.

Shrivathsan · Answer

Yes.. even i picked C

Heseraj · Answer

Hello

Can you please provide a little bid clarification?

Isn't that we might mistake the sides of isosceles triangles and then get the height wrong?

amanvermagmat · Answer

Hi

Length XY is fixed as per the question. A RIGHT isosceles triangle has two legs which are equal and a hypotenuse which is larger than the legs.

So if we are already given that the Right Isosceles triangle has a leg of length XY, the other leg will also be of the length XY and the hypotenuse will be √2 times XY.

So its perimeter is fixed, and can have only one possible value.

Addu.23 · Answer

Bunuel  I came across this question in my unofficial mock exam and got completely clueless. Didn't really understand what the question is asking. Please help!

Fdambro294 · Answer

The simple answer is that out of all the answer choices, the area of a circle that has Chord XY can vary. It all depends on the placement of Chord XY within the Circle.

Chord XY can be Length 4.

Case 1: chord XY is the Diameter of the Circle. The Circle’s Area is less than the area of the Circle in Case 2

Case 2: Chord XY connects 2 opposite-side Points of the Circle that are closer to the Circle’s perimeter.

In this Case 2, the chord XY is NOT the Diameter. The Case 2’s Diameter is greater than the Diameter of the Circle in case 1 —->thus the Area is greater (and most importantly different)

Why the other answers are wrong:

-A-
If the Circle’s diameter = XY, then the Circle and its corresponding Circumference will be fixed around the Diameter. Can not change.

-B-
If the Diagonal of the Square is XY, then the Square’s Area is fixed around the 2 Congruent Diagonals Equal to Length XY that are Perpendicular Bisectors of each other. Can not change.

-C-

The Right Isosceles Triangle always has its 3 Side lengths fixed based on a constant Ratio. Given the Side Length of 1 of the Legs (in which both Legs have equal lengths), the Perimeter of the Figure is fixed. Can not change.

-E-

An equilateral triangle has all 3 of its sides of equal length. Given 1 side length XY, we therefore know all 3 Side Lengths of the triangle. The figure’s area becomes fixed once the Side Lengths are known. Can not change.

Answer -D-

Posted from my mobile device

bumpbot · Answer

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If points X and Y are two distinct points in the coordinate plane, whi

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If points X and Y are two distinct points in the coordinate plane, whi

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