Coordinate Geometry

$\sqrt{5}$adkg

What is the x-coordinate of every point that lies on a vertical line through C?

2. Which of the following points lie on a horizontal line through C?

(2, 4) (2, -4) (0, 4)

(4, 3) (15, 4) (-4, 3)

 3. Find OD and BF.

 In Exercises 4-9 state: 

a. the coordinates of T.

b. the lengths of the legs of the right triangle.

c. the length of the segment shown.

 In Exercises 4-9 state: 

a. the coordinates of T.

b. the lengths of the legs of the right triangle.

c. the length of the segment shown.

In Exercises 4-9 state: 

a. the coordinates of T.

b. the lengths of the legs of the right triangle.

c. the length of the segment shown.

 In Exercises 4-9 state: 

a. the coordinates of T.

b. the lengths of the legs of the right triangle.

c. the length of the segment shown.

In Exercises 4-9 state: 

a. the coordinates of T.

b. the lengths of the legs of the right triangle.

c. the length of the segment shown.

In Exercises 4-9 state: 

a. the coordinates of T.

b. the lengths of the legs of the right triangle.

c. the length of the segment shown.

Find the distance between the two points. If necessary, you may draw graphs but you shouldn’t need to use the distance formula.

Find the distance between the two points. If necessary, you may draw graphs but you shouldn’t need to use the distance formula.

Find the distance between the two points. If necessary, you may draw graphs but you shouldn’t need to use the distance formula.

Find the distance between the two points. If necessary, you may draw graphs but you shouldn’t need to use the distance formula.

Use the distance formula to find the distance between the two points.

Use the distance formula to find the distance between the two points.

Use the distance formula to find the distance between the two points.

 (-8, 6) and (0, 0)

Use the distance formula to find the distance between the two points.

Use the distance formula to find the distance between the two points.

Use the distance formula to find the distance between the two points.

10. Find the distance between the points named. Give all answers in simplest

form.

1.  (0, 0) and (5, -3).
2.  (3, -2) and (-5, -2).
3.  (4, 4) and (-3, -3).

10. Find the distance between the points named. Give all answers in simplest

form.

1.  (0, 0) and (5, -3).
2.  (3, -2) and (-5, -2).

      3. (4, 4) and (-3, -3).

Find the distance between the points named. Use any method you choose.

 (-2, -2) and (5, 7)

11. Find the center and the radius of each circle.

a. ${(x-2)}^2+y^2=1$

b. ${(x+2)}^2+{(y-8)}^2=16$

c. $x^2+{(y+5)}^2=112$

d. ${(x+3)}^2+{(y+7)}^2=14$

Find the distance between the points named. Use any method you choose.

12, Find an equation of the circle that has the given center and radius

a. Center (2, 5); radius 3.

b. Center (-2, 0); radius 5.

c. Center (-2, 3); radius 10. 

d. Center (j, 4); radius n.

Find the distance between the points named. Use any method you choose.

12. (-4, -1) and (-4, 3)

Given points A, B, and C. Find AB, BC, and AC. Are A, B, and C collinear?

If so, which point lies between the other two?

13. A(0, 3), B(-2, 1), C(3, 6)

Given points A, B, and C. Find AB, BC, and AC. Are A, B, and C collinear?

If so, which point lies between the other two?

14. A(5, -5), B(0, 5), C(2, 1)

Given points A, B, and C. Find AB, BC, and AC. Are A, B, and C collinear?

If so, which point lies between the other two?

15. A(-5, 6), B(0, 2), C(3, 0)

Given points A, B, and C. Find AB, BC, and AC. Are A, B, and C collinear?

If so, which point lies between the other two?

16. A(3, 4), B(-3, 0), C(-1, 1)

Find the center and radius of each circle.

${\left(x+3\right)}^2+y^2=49$

Find the center and radius of each circle.

${\left(x+7\right)}^2+{\left(y-8\right)}^2=\frac{36}{25}$

Find the center and radius of each circle.

${\left(x-j\right)}^2+{\left(y+14\right)}^2=17$

Find the center and radius of each circle.

${\left(x+a\right)}^2+{\left(y-b\right)}^2=c^2$

Write an equation of the circle that has the given center and radius.$C(3,0);r=8$

Write an equation of the circle that has the given center and radius.

$C(0,0);r=6$

Write an equation of the circle that has the given center and radius.

$C(-4,-7);r=5$.

Write an equation of the circle that has the given center and radius.

$C(-2,5);r=\frac{1}{3}$

Write an equation of the circle that has the given center and radius.

$C(-2,5);r=\frac{1}{3}$

Sketch the graph of 

${\left(x-3\right)}^2+{\left(y+4\right)}^2=36$

Sketch the graph of 

${\left(x-2\right)}^2+{\left(y-5\right)}^2\le 9$

Show that the triangle with vertices $A\left(-3,4\right),M\left(3,1\right),\text{ and }Y\left(0,2\right)$ is an isosceles triangle.

In Exercises 27-32 find and then compare lengths of segments.

 Quadrilateral TAUL has vertices T(4, 6), A(6, -4), U(~4, -2), and L(-2, 4), Show that the diagonals are congruent.

 In Exercises 27-32 find and then compare lengths of segments.

 Quadrilateral TAUL has vertices T(4, 6), A(6, -4), U(~4, -2), and L(-2, 4), Show that the diagonals are congruent.

In Exercises 27-32 find and then compare lengths of segments.

 Triangles JAN and RFK have vertices J(-2, -2), A(4, -2), M(2, 2), R(8, 1), F(S, 4), and K(6, 3). Show that triangle JAN is similar to triangle RFK.

In Exercises 27-32 find and then compare lengths of segments.

 The vertices of triangle KAT and triangle JES are K(3, -1), A(2, 6), T(5, 1), I(-4, 1), E(-3, -6), and S(-6, -1). What word best describes the relationship between triangle KAT and triangle IES?

 In Exercises 27-32 find and then compare lengths of segments.

 Find the area of the rectangle with vertices B(8, 0). T(2, -9), R(-1, -7), and C(5, 2).

 In Exercises 27-32 find and then compare lengths of segments.

 Show that the triangle with vertices D(0, 0), E(3, 1), and F(-2, 6) is a right triangle, then find the area of the triangle.

There are twelve points, each with integer coordinates, that are 10 units from the origin. List the points. (Hint: Recall the 6, 8, 10 right triangle.)