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Tenth Grade (Grade 10) Coordinate Geometry Questions

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Grade 10 Coordinate Geometry CCSS: HSG-GPE.B.4
For the circle centered at [math](-1,3)[/math] with radius 3, which of the following is true about the point [math](0.5, 0.2) ?[/math]
  1. It lies on the circle.
  2. It lies in the circle.
  3. It lies outside the circle.
  4. Not enough information.
Grade 10 Coordinate Geometry
Grade 10 Coordinate Geometry CCSS: HSG-GPE.B.4
Ellen is given four points and their coordinates: [math]A (-2,0); B (4,4); C (7,3); D(1,-1)[/math]. She is asked to show whether these points form a parallelogram. In order to do so, she finds the midpoints of [math]bar{AC}[/math] and [math]bar{BD}[/math]. She finds they are both [math](5/2, 3/2)[/math]. She reasons that, since the midpoints of [math]bar{AC}[/math] and [math]bar{BD}[/math] (the diagonals of the quadrilateral) are coincident, these line segments intersect at each other's midpoints and thus bisect each other. Therefore, she concludes that [math]ABCD[/math] is a parallelogram. Is she correct, and why?
  1. No, she made a calculation error, and the midpoints of [math]bar{AC}[/math] and [math]bar{BD}[/math] are not the same.
  2. No, she must show that both sets of opposite sides are parallel.
  3. No, her reasoning is incorrect. She must find the equations of lines [math]\stackrel{leftrightarrow}{AC}[/math] and [math]\stackrel{leftrightarrow}{BD}[/math], find their intersection point, [math]P[/math], and then see if [math]bar{AP}, bar{PC}[/math] are congruent, and then if [math]bar{BP}, bar{DP}[/math] are congruent.
  4. Yes, this sufficiently shows that [math]ABCD[/math] is a parallelogram.
Grade 10 Coordinate Geometry
If a triangle has vertices located at the coordinates (6, 7), (8, 1), and (1, 2), where is the circumcenter located?
  1. [math](31/6, 37/3)[/math]
  2. [math](1/8, 7/8)[/math]
  3. [math](19/4, 13/4)[/math]
  4. [math](29/8, -37/8)[/math]
Grade 10 Coordinate Geometry
Find the coordinates of the circumcenter of the triangle with vertices given by the coordinates (4, -2), (-3, -5), and (-3, -1).
  1. [math](-3, 14/3)[/math]
  2. [math](2/7, -3)[/math]
  3. [math](5/7, -3)[/math]
  4. [math](17/7, -2)[/math]
Grade 10 Coordinate Geometry
What are the coordinates of the circumcenter of a triangle with vertices located at (-4, 6), (2, 10), and (-2, -2)?
  1. [math](15/7, 23/7)[/math]
  2. [math](24/7, 20/7)[/math]
  3. [math](5/13, 37/13)[/math]
  4. [math](-42/11, 58/11)[/math]
Grade 10 Coordinate Geometry
Find the location of the centroid of a triangle with vertices given by the following coordinates: (1, 9), (7, 1), and (1, 1).
  1. [math](17/3 ,1)[/math]
  2. [math](1, 17/3)[/math]
  3. [math](8/3, 10/3)[/math]
  4. [math](3,11/3)[/math]
Grade 10 Coordinate Geometry
Find the location of the centroid of the triangle whose vertices are located at (1, 5), (5, -2), and (8, 0).
  1. [math](6, -1/3)[/math]
  2. [math](2, 11/3)[/math]
  3. [math](14/3, 1)[/math]
  4. [math](7/3, 10/3)[/math]
Grade 10 Coordinate Geometry
For the triangle whose vertices are located at (-5, -1), (3, 0), and (8, 1), what are the coordinates of its centroid?
  1. [math](10/3, -4/3)[/math]
  2. [math](1,1)[/math]
  3. [math](2,0)[/math]
  4. [math](-1/3, 7/3)[/math]
Grade 10 Coordinate Geometry
Find the coordinates of the orthocenter of a triangle whose vertices are located at (8, 9), (-4, 5), and (3, -4).
  1. [math](165/14, -15/14)[/math]
  2. [math](10/17, 55/17)[/math]
  3. [math](107/22, 35/22)[/math]
  4. [math](-46/17, 223/17)[/math]
Grade 10 Coordinate Geometry
What is the location of the orthocenter of a triangle whose vertices are given by the coordinates (0, -1), (4, 1), and (-3, -6)?
  1. [math](-11, 10)[/math]
  2. [math](-1/3, -2/3)[/math]
  3. [math](-11/3, -14/3)[/math]
  4. [math](10,-11)[/math]
Grade 10 Coordinate Geometry
What are the coordinates of the orthocenter of a triangle with vertices given by coordinates (3, 3), (2, 9), and (6, 5)?
  1. [math](9/2, 21/4)[/math]
  2. [math](-3/2,15/4)[/math]
  3. [math](24/5, 24/5)[/math]
  4. [math](-22/3, 25/9)[/math]
Grade 10 Coordinate Geometry CCSS: HSG-GPE.B.6
If a segment has one endpoint at (9, 8) and a midpoint at (0, 9), what are the coordinates of the other endpoint?
  1. [math] (-9,10) [/math]
  2. [math](1 1/2,-1)[/math]
  3. [math](4 1/2,-1/2)[/math]
  4. [math](8 1/2,4 1/2)[/math]
Grade 10 Coordinate Geometry CCSS: HSG-GPE.B.6
Grade 10 Coordinate Geometry
A line has a slope of [math]5/3[/math] and crosses the y-axis at (0, -3). Which equation represents the line?
  1. [math]y = - 5/3 x - 3[/math]
  2. [math]y = - 5/3 x + 3[/math]
  3. [math]y = 5/3 x - 3[/math]
  4. [math]y = 5/3 x + 3[/math]
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