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

$$(-2,-3) \text { and }(-2,4)$$

Amrita B.

Numerade Educator

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

$$(3,3) \text { and }(-2,3)$$

Kami D.

Numerade Educator

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

$$(3,-4) \text { and }(-1,-4)$$

Amrita B.

Numerade Educator

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

$$(0,0) \text { and }(3,4)$$

Kami D.

Numerade Educator

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

$$(-6,-2) \text { and }(-7,-5)$$

Amrita B.

Numerade Educator

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

$$(3,2) \text { and }(5,-2)$$

Kami D.

Numerade Educator

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

$$(-8,6) \text { and }(0,0)$$

Amrita B.

Numerade Educator

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

$$(12,-1) \text { and }(0,-6)$$

Kami D.

Numerade Educator

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

$$(5,4) \text { and }(1,-2)$$

Amrita B.

Numerade Educator

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

$$(-2,-2) \text { and }(5,7)$$

Kami D.

Numerade Educator

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

$$(-2,3) \text { and }(3,-2)$$

Amrita B.

Numerade Educator

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

$$(-4,-1) \text { and }(-4,3)$$

Kami D.

Numerade Educator

Given points $A, B,$ and $C .$ Find $A B, B C,$ and $A C .$ Are $A, B,$ and $C$ collinear? If so, which point lies between the other two?

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

Amrita B.

Numerade Educator

Given points $A, B,$ and $C .$ Find $A B, B C,$ and $A C .$ Are $A, B,$ and $C$ collinear? If so, which point lies between the other two?

$$A(5,-5), B(0,5), C(2,1)$$

Kami D.

Numerade Educator

Given points $A, B,$ and $C .$ Find $A B, B C,$ and $A C .$ Are $A, B,$ and $C$ collinear? If so, which point lies between the other two?

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

Amrita B.

Numerade Educator

Given points $A, B,$ and $C .$ Find $A B, B C,$ and $A C .$ Are $A, B,$ and $C$ collinear? If so, which point lies between the other two?

$$A(3,4), B(-3,0), C(-1,1)$$

Kami D.

Numerade Educator

Find the center and the radius of each circle.

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

Amrita B.

Numerade Educator

Find the center and the radius of each circle.

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

Kami D.

Numerade Educator

Find the center and the radius of each circle.

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

Amrita B.

Numerade Educator

Find the center and the radius of each circle.

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

Kami D.

Numerade Educator

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

$$C(3,0) ; r=8$$

Amrita B.

Numerade Educator

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

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

Kami D.

Numerade Educator

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

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

Amrita B.

Numerade Educator

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

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

Kami D.

Numerade Educator

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

Show that the triangle with vertices $A(-3,4), M(3,1),$ and $Y(0,-2)$ is isosceles.

Amrita B.

Numerade Educator

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

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

Kami D.

Numerade Educator

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

Triangles $J A N$ and $R F K$ have vertices $J(-2,-2), A(4,-2), N(2,2),$ $R(8,1), F(8,4),$ and $K(6,3)$ . Show that $\triangle J A N$ is similar to $\triangle R F K$ .

Amrita B.

Numerade Educator

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

The vertices of $\triangle K A T$ and $\triangle I E S$ 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 $\triangle K A T$ and $\triangle I E S ?$

Kami D.

Numerade Educator

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 $C(5,2) .$

Amrita B.

Numerade Educator

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.

Kami D.

Numerade Educator

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.)

Amrita B.

Numerade Educator

a. List twelve points, each with integer coordinates, that are 5 units from $(-8,1)$ .

b. Find an equation of the circle containing these points.

Kami D.

Numerade Educator

In Exercises 35-38 find an equation of the circle described and sketch the graph.

The circle has center $(0,6)$ and passes through point $(6,14) .$

Amrita B.

Numerade Educator

In Exercises 35-38 find an equation of the circle described and sketch the graph.

The circle has center $(-2,-4)$ and passes through point $(3,8)$ .

Kami D.

Numerade Educator

In Exercises 35-38 find an equation of the circle described and sketch the graph.

The circle has diameter $\overline{R S}$ where $R$ is $(-3,2)$ and $S$ is $(3,2)$ .

Amrita B.

Numerade Educator

In Exercises 35-38 find an equation of the circle described and sketch the graph.

The circle has center $(p, q)$ and is tangent to the $x$ -axis.

Kami D.

Numerade Educator

a. Find the radii of the circles

$$x^{2}+y^{2}=25 \text { and }(x-9)^{2}+(y-12)^{2}=100$$

b. Find the distance between the centers of the circles.

c. Explain why the circles must be externally tangent.

d. Sketch the graphs of the circles.

Kami D.

Numerade Educator

a. Find the radii of the circles

$$x^{2}+y^{2}=2 \text { and }(x-3)^{2}+(y-3)^{2}=32$$

b. Find the distance between the centers of the circles.

c. Explain why the circles must be internally tangent.

d. Sketch the graphs of the circles.

Kami D.

Numerade Educator

Discover and prove something about the quadrilateral with vertices $R(-1,-6), A(1,-3), Y(11,1),$ and $J(9,-2)$

Amrita B.

Numerade Educator

Discover and prove two things about the triangle with vertices $K(-3,4)$, $M(3,1),$ and $J(-6,-2) .$

Kami D.

Numerade Educator

It is known that $\triangle G H M$ is isosceles. $G$ is point $(-2,-3), H$ is point $(-2,7),$ and the $x$ -coordinate of $M$ is $4 .$ Find all five possible values for the $y$ -coordinate of $M .$

Amrita B.

Numerade Educator

Find the coordinates of the point that is equidistant from $(-2,5),(8,5),$ and $(6,7) .$

Kami D.

Numerade Educator

Find the center and the radius of the circle $x^{2}+4 x+y^{2}-8 y=16$ . (Hint: Express the given equation in the form

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

Amrita B.

Numerade Educator