Coordinate Geometry Hard
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Given the vertices of parallelogram QRST in the standard (x, y) coordinate plane below, what is the area of triangle QRS, in square units?
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24
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28
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48
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60
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80
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The 'Coordinate Geometry Hard' quiz assesses advanced understanding of coordinate geometry principles through problems on area calculation, equation derivation, and slope determination. This quiz is ideal for learners seeking to enhance their analytical skills in mathematics.
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- 2.
In the standard (x, y) coordinate plane, what is the equation of the line that passes through the origin and the point (3, 4)?
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Y = 1/4x + 3/4
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Y = 1/4x - 1/3
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Y = 4/3x
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Y = 1/2x + 3/4
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Y = 9/4x
Correct Answer
A. Y = 4/3xExplanation
slope = 3/4. remember the origin is just the point (0, 0) so you can use the slope formula followed by point slope form: y - y1 = m(x - x1) but if you think about it, b has to be 0 if it goes through the origin!Rate this question:
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- 3.
For what value of n would the following system of equations have an infinite number of solutions?3a + b = 1212a + 4b = 3n
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4
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9
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16
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36
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48
Correct Answer
A. 16Explanation
For infinite solutions, every term in the second equation would have to be a multiple of each term in the first equation. The a and b terms are clearly multiplied by 4. 12*4 = 48. So your equation is 48 = 3n, solve for n.Rate this question:
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- 4.
What is the slope of the line that is perpendicular to the line determined by the equation 7x + 4y = 11?
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-4
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-7/4
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11/4
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4
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4/7
Correct Answer
A. 4/7Explanation
Solve for y - then take the opposite reciprocal of the slope since the line is perpendicularRate this question:
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- 5.
What is the distance in the standard (x, y) coordinate plane between points (0, 1) and (4, 4)?
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A
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B
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C
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D
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E
Correct Answer
A. EExplanation
Distance formula - answer left in radical formRate this question:
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- 6.
In the standard (x, y) coordinate plane, if the x-coordinate of each point on a line is 5 more than half the y-coordinate, what is the slope of the line?
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-5
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-1/2
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1/2
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2
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5
Correct Answer
A. 2Explanation
x = 1/2y + 5. Solve for y and you get y = 2x - 5. This one is hard!Rate this question:
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- 7.
A system of linear equations is shown below.4y = 3x + 12-4y = -3x - 8Which of the following describes the graph of this system of linear equations in the standard (x, y) coordinate plane?
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Two parallel lines with negative slope
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Two parallel lines with positive slope
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A single line with negative slope
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A single line with positive slope
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Two perpendicular lines
Correct Answer
A. Two parallel lines with positive slopeExplanation
The solution is no solution (0 = 4) so the lines are parallel and the slope of each of them is positive 3/4 (in the second one, the two negatives cancel).Rate this question:
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- 8.
In the standard (x, y) coordinate plane, if a square has the vertices (-2, -3), (2, -3) and (2, 1), what is the set of coordinates for the final vertex?
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(2, -1)
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(1, -2)
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(-1, 2)
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(-2, -1)
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(-2, 1)
Correct Answer
A. (-2, 1)Explanation
You just need to sketch this one to see it - don't try and figure it out in your head.Rate this question:
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- 9.
Given that y - 5 = 1/2x + 1 is the equation of a line, at what point does it cross the x-axis?
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-15
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-12
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1
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4
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6
Correct Answer
A. -12Explanation
It crosses the x-axis when y = 0, so 0-5 = 1/2x + 1. solve for x and you should get the right answer.Rate this question:
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Current Version
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Mar 22, 2023Quiz Edited by
ProProfs Editorial Team -
Jun 23, 2010Quiz Created by
Annacabral
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