Section 1
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.$$(-2,-3) \text { and }(-2,4)$$
Find the distance between the two points. If necessary, you may draw graphs but you shouldn't need to use the distance formula.$(3,3)$ and $(-2,3)$
Find the distance between the two points. If necessary, you may draw graphs but you shouldn't need to use the distance formula.$(3,-4)$ and $(-1,-4)$
Find the distance between the two points. If necessary, you may draw graphs but you shouldn't need to use the distance formula.$$(0,0) \text { and }(3,4)$$
Use the distance formula to find the distance between the two points.$$(-6,-2) \text { and }(-7,-5)$$
Use the distance formula to find the distance between the two points.$(3,2)$ and $(5,-2)$
Use the distance formula to find the distance between the two points.$$(-8,6) \text { and }(0,0)$$
Use the distance formula to find the distance between the two points.$$(12,-1) \text { and }(0,-6)$$
Find the distance between the points named. Use any method you choose.$$(5,4) \text { and }(1,-2)$$
Find the distance between the points named. Use any method you choose.$$(-2,-2) \text { and }(5,7)$$
Find the distance between the points named. Use any method you choose.$$(-2,3) \text { and }(3,-2)$$
Find the distance between the points named. Use any method you choose.$$(-4,-1) \text { and }(-4,3)$$
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?$$A(0,3), B(-2,1), C(3,6)$$
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?$$A(5,-5), B(0,5), C(2,1)$$
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?$$A(-5,6), B(0,2), C(3,0)$$
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?$$A(3,4), B(-3,0), C(-1,1)$$
Find the center and the radius of each circle.$$(x+3)^{2}+y^{2}=49$$
Find the center and the radius of each circle.$$(x+7)^{2}+(y-8)^{2}=\frac{36}{25}$$
Find the center and the radius of each circle.$$(x-j)^{2}+(y+14)^{2}=17$$
Find the center and the radius of each circle.$$(x+a)^{2}+(y-b)^{2}=c^{2}$$
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.$$C(-2,5) ; r=\frac{1}{3}$$
Sketch the graph of $(x-3)^{2}+(y+4)^{2}=36$
Sketch the graph of $(x-2)^{2}+(y-5)^{2} \leq 9$
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.
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.
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 $\triangle R F K$
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 $\triangle I E S ?$
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 $C(5,2)$
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.)
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.
Find an equation of the circle described and sketch the graph.The circle has center $(0,6)$ and passes through point $(6,14)$
Find an equation of the circle described and sketch the graph.The circle has center $(-2,-4)$ and passes through point $(3,8)$
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 $(3,2)$
Find an equation of the circle described and sketch the graph.The circle has center $(p, q)$ and is tangent to the $x$ -axis.
a. Find the radii of the circles $x^{2}+y^{2}=25$ 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.
a. Find the radii of the circles $x^{2}+y^{2}=2$ 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.
Discover and prove something about the quadrilateral with vertices $R(-1,-6), A(1,-3), Y(11,1),$ and $J(9,-2)$
Discover and prove two things about the triangle with vertices $K(-3,4)$ $M(3,1),$ and $J(-6,-2)$
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 $M$
Find the coordinates of the point that is equidistant from $(-2,5),(8,5)$ and $(6,7)$
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$$(x-a)^{2}+(y-b)^{2}=r^{2}$$