2011 Korean CSAT Exam #16

Algebra Level 3

Denote three points as the following: P ( x 1 , y 1 ) , Q ( x 2 , y 2 ) , R ( x 3 , y 3 ) P(x_1,y_1), Q(x_2,y_2), R(x_3,y_3) .

Using the diagram above, which of the following inequalities is/are TRUE? ( Do NOT use a calculator. NO CHEATING! )

(1.) 1 2 < x 1 < 1 \quad \dfrac12<x_1<1

(2.) x 2 < 2 x 1 \quad x_2<2x_1

(3.) x 2 ( x 1 − 1 ) > y 1 ( y 2 − 1 ) \quad x_2(x_1-1)>y_1(y_2-1)

(1) only (2) only (3) only (1) and (2) only (1) and (3) only (2) and (3) only (1), (2) and (3) None of them

Inquisitor Math by Inquisitor Math , 20, South Korea

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1 solution

Inquisitor Math
Mar 24, 2021

(2.) x 2 y 2 − x 3 y 3 = 0 x_2y_2-x_3y_3=0 .

This was the original statement. Therefore R was denoted in the original context.

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