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Let A, B and C be three distinct points on the graph of y =x^2 such th 03 Jun 2022, 01:30
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39% (02:53) correct 61% (02:37) wrong based on 44 sessions

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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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Let A, B and C be three distinct points on the graph of y =x^2 such th 09 Sep 2022, 22:41
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Bunuel
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


Are You Up For the Challenge: 700 Level Questions
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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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Let A, B and C be three distinct points on the graph of y =x^2 such th 10 Sep 2022, 01:09
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Bunuel
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
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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 10 Sep 2022, 02:01
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sourodeep

Could you please explain how did you write the area of traingle as 1/2*2X*1?
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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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sourodeep

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 !
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Thanks for the clarification !
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