Relationships… are they proportional? !!!20 POINTS!!!

8) Find the endpoint Cif M is the midpoint of segment CD and M (2, 4) and D (5,7)

Elenna [48]

Answer:

8. c. (-1, -1)

9. a. (-6, -1)

b. True

Step-by-step Explanation:

8. Given the midpoint M(2, 4), and one endpoint D(5, 7) of segment CD, the coordinate pair of the other endpoint C, can be calculated as follows:

let $D(5, 7) = (x_2, y_2)$

$C(?, ?) = (x_1, y_1)$

$M(2, 4) = (\frac{x_1 + 5}{2}, \frac{y_1 + 7}{2})$

Rewrite the equation to find the coordinates of C

$2 = \frac{x_1 + 5}{2}$ and $4 = \frac{y_1 + 7}{2}$

Solve for each:

$2 = \frac{x_1 + 5}{2}$

$2*2 = \frac{x_1 + 5}{2}*2$

$4 = x_1 + 5$

$4 - 5 = x_1 + 5 - 5$

$-1 = x_1$

$x_1 = -1$

$4 = \frac{y_1 + 7}{2}$

$4*2 = \frac{y_1 + 7}{2}*2$

$8 = y_1 + 7$

$8 - 7 = y_1 + 7 - 7$

$1 = y_1$

$y_1 = 1$

Coordinates of endpoint C is (-1, 1)

9. a.Given segment AB, with midpoint M(-4, -5), and endpoint A(-2, -9), find endpoint B as follows:

let $A(-2, -9) = (x_2, y_2)$

$B(?, ?) = (x_1, y_1)$

$M(-4, -5) = (\frac{x_1 + (-2)}{2}, \frac{y_1 + (-9)}{2})$

$-4 = \frac{x_1 - 2}{2}$ and $-5 = \frac{y_1 - 9}{2}$

Solve for each:

$-4 = \frac{x_1 - 2}{2}$

$-4*2 = \frac{x_1 - 2}{2}*2$

$-8 = x_1 - 2$

$-8 + 2 = x_1 - 2 + 2$

$-6 = x_1$

$x_1 = -6$

$-5 = \frac{y_1 - 9}{2}$

$-5*2 = \frac{y_1 - 9}{2}*2$

$-10 = y_1 - 9$

$-10 + 9 = y_1 - 9 + 9$

$-1 = y_1$

$y_1 = -1$

Coordinates of endpoint B is (-6, -1)

b. The midpoint of a segment, is the middle of the segment. It divides the segment into two equal parts. The answer is TRUE.

4 0

4 years ago

Help me please, its due at night today!!!

postnew [5]

Answer:

Step-by-step explanation:

Area of polygon = area of square + area of triangle

Square:

Side = 12 cm

Area of square = side *side

= 12 * 12

= 144 sq.cm

Triangle:

base (b) = 12 cm

Height h = 19 cm

$Area =\frac{1}{2}bh\\\\=\frac{1}{2}*12*19\\$

= 6 * 19

= 114 sq.cm

Area of polygon = 144 + 114 = 258 square cm

4 0

3 years ago

.Challenge: What is the term-to-term rule for this sequence? 1, 5, 13, 29, 61

olya-2409 [2.1K]

Answer:c)21

Step-by-step explanation:

i just took the quiz

6 0

3 years ago

Read 2 more answers

How to equivalent 64 1/2

bagirrra123 [75]

Answer:

129/2

Step-by-step explanation:

1 129

64 --- = -------

2 2

To find the improper fraction, you multiply the denominator by the whole number and then add the numerator. In the end, you put that answer over the starting denominator.

64 X 2 = 128 128 + 1 = 129 129 / 2 is the answer

7 0

3 years ago

What is the quotient in simplified form? State any restrictions on the variable. Show Work.

photoshop1234 [79]

a+2 a +1
= ------- / ------------------
a -5 (a - 3)(a - 5)

a+2 (a - 3)(a - 5)
= ------- * ------------------
a -5 a +1

(a+2)(a - 3)
= ----------------
a +1

a NOT equal 5 and -1

5 0

3 years ago

Read 2 more answers