Questions and Answers
The equation of a line can be found for which of the following situations? (Select all that apply)
Indicate in standard form the equation of the line passing through the points A(4, 1) and B(5, 2).
x - y = 3
Indicate in standard form the equation of the line passing through the points R(3, 3) and S(-6, -6).
x - y = 0
Indicate in standard form the equation of the line passing through the points B(0, 0) and C(4, -4).
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Indicate in standard form the equation of the line passing through the points P(6, 2) and Q(8, -4).
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Indicate in standard form the equation of the line passing through the points M(0, 6) and N(6, 0).
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Indicate in standard form the equation of the line passing through the points E(-2, 2) and F(5, 1).
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Indicate in standard form the equation of the line passing through the points G(4, 6) and H(1, 5).
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Indicate in standard form the equation of the line passing through the points S(1/2, 1) and T(1/2, 4).
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Indicate in standard form the equation of the line passing through the points L(5, 0) and M(0, 5).
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Indicate in standard form the equation of the line passing through the points X(0, 6) and Y(5, 6).
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Indicate in standard form the equation of the line passing through the point A(5, 5) with a slope m = 3.
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Indicate in standard form the equation of the line passing through the point B(6, 2) with a slope m = 1/2.
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Indicate in standard form the equation of the line passing through the point C(0, 4) with a slope m = 0.
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Indicate in standard form the equation of the line passing through the point D(5, -2) with a slope m = 2/5.
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Indicate in standard form the equation of the line passing through the point E(3, 5) with a slope m = undefined.
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Indicate the equation of the line through (2, -1) and parallel to a line with slope of 3/4.
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Indicate the equation of the line through the point (-3, 4) and perpendicular to a line with a given slope.
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Indicate the equation of the line with slope and containing the midpoint of the segment with endpoints (2, -3) and (-6, 5).
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Indicate the equation of the line through the midpoint of and perpendicular to the segment joining (1, 0) and (5, -2).
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Indicate the equation of the line containing the midpoints of the legs of right triangle ABC with vertices A(-5, 5), B(1, 1), C(3, 4).
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Indicate the equation of the line containing the hypotenuse of right triangle ABC with vertices A(-5, 5), B(1, 1), C(3, 4).
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Indicate the equation of the line containing the longer diagonal of a quadrilateral with vertices A(2, 2), B(-2, -2), C(1, -1), D(6, 4).
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Indicate the equation of the line containing the median of the trapezoid with vertices R(-1, 5), S(1, 8), T(7, -2), U(2, 0).
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Indicate the equation of the line containing the altitude to the hypotenuse of a right triangle with vertices P(-1, 1), Q(3, 5), R(5, -5).
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Indicate the equations of the diagonals of a square with vertices A(-3, 3), B(3, 3), C(3, -3), D(-3, -3).
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Study Notes
Situation of Lines
- An equation of a line can be determined if either two points on the line are known or a point on the line and the slope are provided.
Standard Form Equations of Lines
- Line through points A(4, 1) and B(5, 2): x - y = 3
- Line through points R(3, 3) and S(-6, -6): x - y = 0
- Line through points B(0, 0) and C(4, -4): x + y = 0
- Line through points P(6, 2) and Q(8, -4): 3x + y = 20
- Line through points M(0, 6) and N(6, 0): x + y = 6
- Line through points E(-2, 2) and F(5, 1): x + 7y = 12
- Line through points G(4, 6) and H(1, 5): x - 3y = -14
- Line through points S(1/2, 1) and T(1/2, 4): x = 1/2
- Line through points L(5, 0) and M(0, 5): x + y = 5
- Line through points X(0, 6) and Y(5, 6): y = 6
Lines with Given Points and Slopes
- Point A(5, 5) with slope m = 3: 3x - y = 10
- Point B(6, 2) with slope m = 1/2: x + 2y = 10
- Point C(0, 4) with slope m = 0: y = 4 (horizontal line)
- Point D(5, -2) with slope m = 2/5: 2x - 5y = 20
- Point E(3, 5) with slope m = undefined: x = 3 (vertical line)
Specific Line Requirements
- Line through point (2, -1) parallel to slope 3/4: 3x - 4y = 10
- Line through point (-3, 4) perpendicular to another slope: 5x + 2y = -7
- Line with midpoint between points (2, -3) and (-6, 5): 9x - 7y = -25
- Line through the midpoint, perpendicular to points (1, 0) and (5, -2): 2x - y = 7
- Line through midpoints of triangle ABC (A(-5, 5), B(1, 1), C(3, 4)): x + 8y = 22
- Line containing the hypotenuse of triangle ABC: x + 8y = 35
- Line containing the longer diagonal of quadrilateral with vertices A(2, 2), B(-2, -2), C(1, -1), D(6, 4): 3x - 4y = 2
- Line containing the median of trapezoid with vertices R(-1, 5), S(1, 8), T(7, -2), U(2, 0): 10x + 6y = 39
- Line containing the altitude to the hypotenuse of triangle P(-1, 1), Q(3, 5), R(5, -5): x - 5y = -6
- Equations for diagonals of square with vertices A(-3, 3), B(3, 3), C(3, -3), D(-3, -3): x +/- y = 0 (representing both diagonals)
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Description
This quiz covers the various forms of line equations, including standard forms and equations derived from given points and slopes. Test your knowledge on finding the equations of lines based on different scenarios and coordinate points.
