1) Given the number line:
a. Find the length from point \(A\) to point \(B\) (written as as \(AB\))
b. Find the midpoint of \(\overline{AB}\) on the number line.
2) Given the number line:
b. Find the midpoint of \(\overline{AB}\) on the number line.
2) Given the number line:
a. Find \(CD\). (Note regarding notation, when we write \(CD\) without a segment over the top {like \(\overline{CD}\)},
then that means to find the distance from point C to point D.
b. Find the midpoint of \(\overline{CD}\) on the number line.
3) What is its length of the segment in the image below?
then that means to find the distance from point C to point D.
b. Find the midpoint of \(\overline{CD}\) on the number line.
3) What is its length of the segment in the image below?
5) \(U\) is between \(S\) and \(P\). \(SU = 5x - 3\) and \(UP = 8x - 9\) and \(SP = 131\). Find \(x\) and the length of the other two segments.
6) \(O\) is between \(M\) and \(S\). \(MO = 2x + \frac{1}{3}\) and \(OS = 5x + \frac{2}{3}\) and \(MS = 12x - 4\). Find \(x\) and the length of the other two segments.
7) Use the Pythagorean Theorem to determine the length of this segment. Leave your answer in radical form (square root form).
8) Use the Pythagorean Theorem to determine the length of this segment. Leave your answer in radical form (square root form).
9) Use the distance formula to find the length of the segment. Leave your answer in radical form (square root form).
10) Explain how Pythagorean Theorem and the distance formula are similar to each other.
11) What is the midpoint of the segment pictured in problem #9?
12) Use the distance formula to find the length of the segment. Leave your answer in radical form (square root form).
11) What is the midpoint of the segment pictured in problem #9?
12) Use the distance formula to find the length of the segment. Leave your answer in radical form (square root form).
13) Find the midpoint of the segment pictured in problem #12.
14) Use Pythagorean Theorem or the distance formula to find the length of the segment. Leave your answer in radical form (square root form).
14) Use Pythagorean Theorem or the distance formula to find the length of the segment. Leave your answer in radical form (square root form).
15) Find the midpoint of the segment pictured in problem #14.
16) Given the following points, find \(GT\). Leave your answer in radical form.
16) Given the following points, find \(GT\). Leave your answer in radical form.
17) Find the coordinates for \(N\) and \(C\) so that
a. \(NC = \sqrt{10}\)
b. \(NC = \sqrt{13}\)
a. \(NC = \sqrt{10}\)
b. \(NC = \sqrt{13}\)
18) Find the midpoint of the segment pictured in problem #16.
19) Find \(GE\). Leave your answer in radical form. Also, find the midpoint of \(\overline{GE}\).
\(G(-4, -2)\) to \(E(2, 2)\)
20) Point \(M\) is the midpoint of \(\overline{OE}\). If \(O (-4, 13)\) and midpoint \(M (2, 5)\), what is the location of endpoint \(E\)?
21) Use the given endpoint \(T\) and the midpoint \(R\) to find the other endpoint \(Y\). \(T (3, -5)\) and \(R (-7, -2)\).
22) \(\overleftrightarrow{AG}\) bisects \(\overline{KJ}\). Find \(x\). Find \(KY\), find \(YJ\), and find \(KJ\).
19) Find \(GE\). Leave your answer in radical form. Also, find the midpoint of \(\overline{GE}\).
\(G(-4, -2)\) to \(E(2, 2)\)
20) Point \(M\) is the midpoint of \(\overline{OE}\). If \(O (-4, 13)\) and midpoint \(M (2, 5)\), what is the location of endpoint \(E\)?
21) Use the given endpoint \(T\) and the midpoint \(R\) to find the other endpoint \(Y\). \(T (3, -5)\) and \(R (-7, -2)\).
22) \(\overleftrightarrow{AG}\) bisects \(\overline{KJ}\). Find \(x\). Find \(KY\), find \(YJ\), and find \(KJ\).
23) \(\overleftrightarrow{OF}\) bisects \(\overline{TW}\). Find \(z\). Find \(TN\), find \(NW\), and find \(TW\).
24) Determine if the segments pictured are congruent:
25) Determine if the segments are congruent:
\(R(0, -2)\) and \(O(5, -2)\)
\(C(1, -4)\) and \(K(4, 0)\)
26) Find the midpoints of \(\overline{RO}\) and \(\overline{CK}\) from #25.
27) Below is a section of a map of Chicago, Illinois. Using approximate city blocks, how far is it from “theMart” to the “Museum of Contemporary Art?” How many blocks would it take for a crow to fly from the two locations?
\(R(0, -2)\) and \(O(5, -2)\)
\(C(1, -4)\) and \(K(4, 0)\)
26) Find the midpoints of \(\overline{RO}\) and \(\overline{CK}\) from #25.
27) Below is a section of a map of Chicago, Illinois. Using approximate city blocks, how far is it from “theMart” to the “Museum of Contemporary Art?” How many blocks would it take for a crow to fly from the two locations?
28) A seamstress would like to cut a piece of fabric in half. Where should the seamstress cut?
29) Using a direct route, how far is it from Naperville Central High School to Benedictine University. Please round your answer to the nearest foot.
30) Is the midway point of the path directly from Central to Benedictine to the left or right of Olesen Dr.?
31) A grid is placed over a map of the state of Illinois. If each grid mark is equivalent to \(36\) miles, what is the straight line distance (also known as the distance “As the crow flies”) from Naperville to St. Louis, MO?
31) A grid is placed over a map of the state of Illinois. If each grid mark is equivalent to \(36\) miles, what is the straight line distance (also known as the distance “As the crow flies”) from Naperville to St. Louis, MO?
Review
32) Find the equation of the line through \((-3, 6)\) and \((7, 11)\)
33) Solve \(x^2 = 16\)
34) Solve \(x^2 - 11 = 0\)
32) Find the equation of the line through \((-3, 6)\) and \((7, 11)\)
33) Solve \(x^2 = 16\)
34) Solve \(x^2 - 11 = 0\)