Question

vocabulary - match the letter of the vocabulary term to its description. write the matching letter in each blank. use each term only once. an angle with a measure of 180 degrees. angles with a sum of 180 degrees. points that can be found on the same line. an angle with a measure of 90 degrees. to split or divide into two equal sections. angles with a sum of 90 degrees. an angle with a measure between 0 and 90 degrees. the sum of all of the sides of a polygon. an angle with a measure between 90 and 180 degrees. two or more figures or objects that are the same shape and same size. word bank: complementary, supplementary, right angle, d - straight angle, e - obtuse angle, acute angle, g - bisect, h - perimeter, j - collinear, k - congruent. midpoint formula: ($\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2}$). distance formula: $ab = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. 1) $tv$ has endpoints (-4,6) and (8,-12). what is the approximate length of the segment? a. (2,-3) b. 22.4 c. 13.4 d. 21.6. 2) find the midpoint, m, of $\overline{ab}$ with coordinates a (2,10) and b (18,-18). a. (6,0) b. (10,-4) c. (20,-8) d. 32.2. 3) find the length of $\overline{bc}$. a. 21.5 b. 32 c. 54 d. 75

Explanation:

Step1: Identify the distance - formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For the endpoints of \(\overline{TV}\) where \(x_1=-4,y_1 = 6,x_2 = 8,y_2=-12\), we substitute these values into the formula:
\[d=\sqrt{(8-(-4))^2+((-12 - 6))^2}=\sqrt{(8 + 4)^2+(-18)^2}=\sqrt{12^2+(-18)^2}=\sqrt{144 + 324}=\sqrt{468}\approx21.6\]

Step2: Identify the mid - point formula

The mid - point formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\).
For points \(A(2,10)\) and \(B(18,-18)\), we substitute \(x_1 = 2,y_1=10,x_2 = 18,y_2=-18\) into the formula:
\[M=(\frac{2+18}{2},\frac{10+(-18)}{2})=(\frac{20}{2},\frac{10 - 18}{2})=(10,-4)\]

Step3: Find the length of \(\overline{BC}\)

From the number - line, if the coordinate of \(A\) is \(43\), the coordinate of \(B\) is \(11\), and we assume the coordinate of \(C\) is \(0\) (not given explicitly but we can calculate the length based on the relative position on the number - line). The length of \(\overline{BC}\) is \(11\) (assuming \(C\) is at \(0\) and \(B\) is at \(11\)). But if we assume the distance from \(C\) to \(B\) is what we need to find, and we know the distance from \(C\) to \(A\) and \(B\) to \(A\), the length of \(\overline{BC}=43 - 11=32\)

Answer:

1. D. 21.6
2. B. (10, - 4)
3. B. 32