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Let A, B and C be three distinct points on the graph of y =x^2 such th

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Let A, B and C be three distinct points on the graph of y =x^2 such th [#permalink] New post   03 Jun 2022, 01:30
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Let A, B and C be three distinct points on the graph of y =x^2 such that line AB is parallel to the x-axis and triangle ABC is a right triangle with area 2008. What is the sum of the digits of the y-coordinate of C?

(A) 16
(B) 17
(C) 18
(D) 19
(E) 20



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C
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Re: Let A, B and C be three distinct points on the graph of y =x^2 such th [#permalink] New post   02 Sep 2022, 15:06
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where do you put C on the graph to make a right triangle?
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Re: Let A, B and C be three distinct points on the graph of y =x^2 such th [#permalink] New post   03 Sep 2022, 01:01
Can you please post the official answer explanation for reference?
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Re: Let A, B and C be three distinct points on the graph of y =x^2 such th [#permalink] New post   09 Sep 2022, 12:39
Can we expect a question on the GMAT of such level?
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Let A, B and C be three distinct points on the graph of y =x^2 such th [#permalink] New post   09 Sep 2022, 22:41
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Bunuel wrote:
Let A, B and C be three distinct points on the graph of y =x^2 such that line AB is parallel to the x-axis and triangle ABC is a right triangle with area 2008. What is the sum of the digits of the y-coordinate of C?

(A) 16
(B) 17
(C) 18
(D) 19
(E) 20



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The right angle is possible only at point C.

We can equate the slopes of the two lines AC and AB to obtain a relationship between the coordinates of point A and point B and point C.

Once that's obtained, we can find the height of the triangle and compute the area.

The working has been shown in the attached image below.

Option C
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Re: Let A, B and C be three distinct points on the graph of y =x^2 such th [#permalink] New post   10 Sep 2022, 01:09
gmatophobia wrote:
Bunuel wrote:
Let A, B and C be three distinct points on the graph of y =x^2 such that line AB is parallel to the x-axis and triangle ABC is a right triangle with area 2008. What is the sum of the digits of the y-coordinate of C?

(A) 16
(B) 17
(C) 18
(D) 19
(E) 20





The right angle is possible only at point C.

We can equate the slopes of the two lines AC and AB to obtain a relationship between the coordinates of point A and point B and point C.

Once that's obtained, we can find the height of the triangle and compute the area.

The working has been shown in the attached image below.

Option C




Could you please explain how did you write the area of traingle as 1/2*2X*1?
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Let A, B and C be three distinct points on the graph of y =x^2 such th [#permalink] New post   10 Sep 2022, 02:01
sourodeep wrote:
Could you please explain how did you write the area of traingle as 1/2*2X*1?


Area of triangle is \(\frac{1}{2} * base * height\)

Base = Change in x intercept = AB = x-(-x) = 2x

Height = Change in y intercept = \((x^2)-(x^2-1)\) = 1

Area of triangle is \(\frac{1}{2} * 2x * 1\)

Hope this clarifies !
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Re: Let A, B and C be three distinct points on the graph of y =x^2 such th [#permalink] New post   10 Sep 2022, 02:04
gmatophobia wrote:
sourodeep wrote:
Could you please explain how did you write the area of traingle as 1/2*2X*1?


Area of triangle is \(\frac{1}{2} * base * height\)

Base = change is x intercept = AB = x-(-x) = 2x

Height = Change in y intercept = \((x^2)-(x^2-1)\) = 1

Area of triangle is \(\frac{1}{2} * 2x * 1\)

Hope this clarifies !


Thanks for the clarification !
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Re: Let A, B and C be three distinct points on the graph of y =x^2 such th [#permalink] New post   14 Mar 2024, 20:31
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