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You can create printable tests and worksheets from these Grade 10 Coordinate Geometry questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.

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Grade 10 Coordinate Geometry CCSS: HSG-GPE.B.4
For the circle centered at $(-1,3)$ with radius 3, which of the following is true about the point $(0.5, 0.2) ?$
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 CCSS: HSG-GPE.B.6
Grade 10 Coordinate Geometry CCSS: HSG-GPE.B.4
Ellen is given four points and their coordinates: $A (-2,0); B (4,4); C (7,3); D(1,-1)$. She is asked to show whether these points form a parallelogram. In order to do so, she finds the midpoints of $bar{AC}$ and $bar{BD}$. She finds they are both $(5/2, 3/2)$. She reasons that, since the midpoints of $bar{AC}$ and $bar{BD}$ (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 $ABCD$ is a parallelogram. Is she correct, and why?
1. No, she made a calculation error, and the midpoints of $bar{AC}$ and $bar{BD}$ 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 $\stackrel{leftrightarrow}{AC}$ and $\stackrel{leftrightarrow}{BD}$, find their intersection point, $P$, and then see if $bar{AP}, bar{PC}$ are congruent, and then if $bar{BP}, bar{DP}$ are congruent.
4. Yes, this sufficiently shows that $ABCD$ is a parallelogram.
If a triangle has vertices located at the coordinates (6, 7), (8, 1), and (1, 2), where is the circumcenter located?
1. $(31/6, 37/3)$
2. $(1/8, 7/8)$
3. $(19/4, 13/4)$
4. $(29/8, -37/8)$
Find the coordinates of the circumcenter of the triangle with vertices given by the coordinates (4, -2), (-3, -5), and (-3, -1).
1. $(-3, 14/3)$
2. $(2/7, -3)$
3. $(5/7, -3)$
4. $(17/7, -2)$
What are the coordinates of the circumcenter of a triangle with vertices located at (-4, 6), (2, 10), and (-2, -2)?
1. $(15/7, 23/7)$
2. $(24/7, 20/7)$
3. $(5/13, 37/13)$
4. $(-42/11, 58/11)$
Find the location of the centroid of a triangle with vertices given by the following coordinates: (1, 9), (7, 1), and (1, 1).
1. $(17/3 ,1)$
2. $(1, 17/3)$
3. $(8/3, 10/3)$
4. $(3,11/3)$
Find the location of the centroid of the triangle whose vertices are located at (1, 5), (5, -2), and (8, 0).
1. $(6, -1/3)$
2. $(2, 11/3)$
3. $(14/3, 1)$
4. $(7/3, 10/3)$
For the triangle whose vertices are located at (-5, -1), (3, 0), and (8, 1), what are the coordinates of its centroid?
1. $(10/3, -4/3)$
2. $(1,1)$
3. $(2,0)$
4. $(-1/3, 7/3)$
Find the coordinates of the orthocenter of a triangle whose vertices are located at (8, 9), (-4, 5), and (3, -4).
1. $(165/14, -15/14)$
2. $(10/17, 55/17)$
3. $(107/22, 35/22)$
4. $(-46/17, 223/17)$
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. $(-11, 10)$
2. $(-1/3, -2/3)$
3. $(-11/3, -14/3)$
4. $(10,-11)$
What are the coordinates of the orthocenter of a triangle with vertices given by coordinates (3, 3), (2, 9), and (6, 5)?
1. $(9/2, 21/4)$
2. $(-3/2,15/4)$
3. $(24/5, 24/5)$
4. $(-22/3, 25/9)$
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. $(-9,10)$
2. $(1 1/2,-1)$
3. $(4 1/2,-1/2)$
4. $(8 1/2,4 1/2)$
Grade 10 Coordinate Geometry CCSS: HSG-GPE.B.6
A line has a slope of $5/3$ and crosses the y-axis at (0, -3). Which equation represents the line?
1. $y = - 5/3 x - 3$
2. $y = - 5/3 x + 3$
3. $y = 5/3 x - 3$
4. $y = 5/3 x + 3$