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A triangle ABC drawn on the coordinate plane has one side determined
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30 Aug 2022, 09:08
30 Aug 2022, 09:08
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46% (01:55) wrong based on 13 sessions
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A triangle ABC drawn on the coordinate plane has one side determined by points A = (1,3) and B = (5,6). The slope of the line BC is −3, while the slope of the line AC = 0. The coordinates of point C are
A (4,6)
B (1,18)
C (3,7)
D (6,3)
E (1,6)
A (4,6)
B (1,18)
C (3,7)
D (6,3)
E (1,6)
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
A triangle ABC drawn on the coordinate plane has one side determined
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31 Aug 2022, 06:51
31 Aug 2022, 06:51
1
Carcass wrote:
A triangle ABC drawn on the coordinate plane has one side determined by points A = (1,3) and B = (5,6). The slope of the line BC is −3, while the slope of the line AC = 0. The coordinates of point C are
A (4,6)
B (1,18)
C (3,7)
D (6,3)
E (1,6)
A (4,6)
B (1,18)
C (3,7)
D (6,3)
E (1,6)
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
Solution -
Here, the points A = (1,3) and B = (5,6) are given.
It is also given that the slope of the line BC is −3, while the slope of the line AC = 0.
Slope of a line = (y2 - y1) / (x2 - x1)
To find the coordinates of point C, we can go by EACH option.
Only answer choice D i.e., (6,3) fulfils the conditions given in the question.
So, the correct answer is D
A triangle ABC drawn on the coordinate plane has one side determined
[#permalink]
31 Aug 2022, 09:04
31 Aug 2022, 09:04
1
Carcass wrote:
A triangle ABC drawn on the coordinate plane has one side determined by points A = (1,3) and B = (5,6). The slope of the line BC is −3, while the slope of the line AC = 0. The coordinates of point C are
A (4,6)
B (1,18)
C (3,7)
D (6,3)
E (1,6)
A (4,6)
B (1,18)
C (3,7)
D (6,3)
E (1,6)
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
If the slope of line AC is 0, we know immediately that the y-coordinate of point C is 3. Why is that true? Because if the slope is zero, the equation of the line in which both points lie is an horizontal line that passes through the point y=3, whose value of y does not change when X changes. Therefore, both points share the same y-coordinate.
Due to the fact that we already figured out the value of y, we now have find the x-coordinate of point C. Using the slope euation, we know that:
\(\frac{(y_{2} - y_{1})}{(x_{2}-x_{1})} = -3\)
\(\frac{(B_{y} - C_{y})}{(B_{x}-C_{x})} = -3\)
\(\frac{(6 - 3)}{(5-C_{x})} = -3\)
Doing some algebra:
\(C_{x} = 6. \)
Therefore, point C is (6,3), being Option D the correct answer.
