Mathematics, 22.11.2020 08:40 norahfrost

9. The coordinates of the endpoints of segments are given below. Are the two line segments
parallel, perpendicular, or neither? Justify
your answer.
a) S(-4, -1), T(-1,5) and U(1,1), V(5, -1)
b) B(-6, -2), C(-3, 3) and D(2,0), E(5,5)
c) N(-6,2), P(--3, -4) and Q(1, -3), R(3, 4)
d) G(-2,5), H(4,1) and J(1, –4), K(7,0)
help is much appreciated

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Answer from: Lalagrl

a. ST and UV are perpendicular lines.

b. BC and DE are parallel.

c. NP and QR are neither parallel nor perpendicular.

d. GH and JK are parallel.

Step-by-step explanation:

Slopes are used to calculate steepness of a line. Slopes are also used to check if two lines are parallel, perpendicular or neither.

When two lines are parallel, their slopes are equal.

When two lines are perpendicular, product of slopes of both lines is -1

Slope is given by the formula:

$m = \frac{y_2-y_1}{x_2-x_1}$

a) S(-4, -1), T(-1,5) and U(1,1), V(5, -1)

$Slope\ of\ ST = \frac{5+1}{-1+4} = \frac{6}{3} = 2\\Slope\ of\ UV = \frac{-1-1}{5-1} = \frac{-2}{4} = -\frac{1}{2}$

Now,

$(Slope\ of\ ST)(Slope\ of\ UV) \\= 2 * -\frac{1}{2}\\=-1$

ST and UV are perpendicular lines.

b) B(-6, -2), C(-3, 3) and D(2,0), E(5,5)

$Slope\ of\ BC = \frac{3+2}{-3+6} = \frac{5}{3}\\Slope\ of\ DE = \frac{5-0}{5-2} = \frac{5}{3}$

As the slopes of two lines is equal, BC and DE are parallel.

c) N(-6,2), P(--3, -4) and Q(1, -3), R(3, 4)

$Slope\ of\ NP = \frac{-4-2}{-3+6} = \frac{-6}{3} = -2\\Slope of\ QR = \frac{4+3}{3-2} = \frac{7}{2}$

NP and QR are neither parallel nor perpendicular.

d) G(-2,5), H(4,1) and J(1, –4), K(7,0)

$Slope\ of\ GH = \frac{1-5}{4+2} = \frac{-4}{6} = -\frac{2}{3}\\Slope\ of\ JK = \frac{0-4}{7-1}= \frac{-4}{6} = -\frac{2}{3}$

GH and JK are parallel.

Hence,

a. ST and UV are perpendicular lines.

b. BC and DE are parallel.

c. NP and QR are neither parallel nor perpendicular.

d. GH and JK are parallel.

Answer from: Quest

(a) common ratio in the given sequence is, 3

(b) $6.973568802 \times 10^9$ push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

$a_n = a_1r^{n-1}$ , where r is the common ratio between the successive terms and $a_1$ is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term $(a_1) = 6$

then;

$a_n = a_ 1 \cdot r^{n-1}$

$a_{20} = 6 \cdot 3^{20-1}$

simplify:

$a_{20} = 6.973568802 \times 10^9$

therefore, $6.973568802 \times 10^9$ push ups will do kendall do on the 20th week

Answer from: Quest

to find the perimeter, you add up all the lengths of the sides. in this case you would have to add up 18+22+40+80 which equals 160.

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