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07 Oct 2021, 06:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
74% (02:28) correct
26%
(02:19)
wrong
based on 104
sessions
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In the standard xy-coordinate plane, the xy-pairs (0, 2) and (2, 0) define a line, and the xy-pairs (-2, -1) and (2, 1) define another line. At which of the following points do the two lines intersect?
(A) \([\frac{4}{3}, \frac{2}{3}]\)
(B) \([\frac{3}{2}, \frac{4}{3}]\)
(C) \([-\frac{1}{2}, \frac{3}{2}]\)
(D) \([\frac{3}{4}, -\frac{2}{3}]\)
(E) \([-\frac{3}{4}, -\frac{2}{3}]\)
(A) \([\frac{4}{3}, \frac{2}{3}]\)
(B) \([\frac{3}{2}, \frac{4}{3}]\)
(C) \([-\frac{1}{2}, \frac{3}{2}]\)
(D) \([\frac{3}{4}, -\frac{2}{3}]\)
(E) \([-\frac{3}{4}, -\frac{2}{3}]\)
Capakki
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07 Oct 2021, 11:26
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Could solve using traditional method.
using 2 point formula the equations for the 2 lines are: y= (-x)+2 & 2y=x.
Solving these, the point of intersection is (4/3,2/3) (Option A)
I Need a shorter approach.
using 2 point formula the equations for the 2 lines are: y= (-x)+2 & 2y=x.
Solving these, the point of intersection is (4/3,2/3) (Option A)
I Need a shorter approach.
15 Oct 2021, 10:13
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Bunuel
Taking the first two points and forming the equation \(y = -x +2 \)
Taking the second two points and forming the equation \( y = \frac{1}{2}x +1\)
Solving these ->\( x= \frac{2}{3}\) , \(y = \frac{4}{3}\)
It seems in choice A \(x \) and \(y\) are reversed !
Point of intersection \(\frac{2}{3}, \frac{4}{3}\)
IMO option A should be \(\frac{2}{3}, \frac{4}{3}\)
