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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 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
Find the distance between (-4,-3) and (-8,7).
  1. [math]sqrt(160)[/math]
  2. [math]sqrt(116)[/math]
  3. [math]4[/math]
  4. [math]sqrt(14)[/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]
Grade 10 Coordinate Geometry CCSS: HSG-GPE.B.6
Grade 10 Coordinate Geometry
[math]((x_1+x_2)/2),((y_1+y_2)/2)[/math]
  1. Midsegment
  2. Sides + Diagonals
  3. Distance Formula
  4. Equation of a Circle
Grade 10 Coordinate Geometry
Grade 10 Coordinate Geometry
Grade 10 Coordinate Geometry
Find the distance between (12,8) and (4,2).
  1. 14 units
  2. 100 units
  3. 10 units
  4. -10 units
Grade 10 Coordinate Geometry
Find the distance between (-8,-8) and (4,8).
  1. 4
  2. 2
  3. [math]sqrt(28)[/math]
  4. 20
Grade 10 Coordinate Geometry
Find the midpoint between (-1,6) and (-6,-1).
  1. [math](2 1/2, -3 1/2)[/math]
  2. [math](-3 1/2, 2 1/2)[/math]
  3. [math](-11,-8)[/math]
  4. [math](2 1/2, 3 1/2)[/math]
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