Question 6 pleaseeee

Determine which of the lines are parallel and which of the lines are perpendicular. Select all of the statements that are true.

slega [8]

Answers:

Line A is parallel to line D.

Line A is perpendicular to line C.

Line C is perpendicular to line D.

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Explanation:

Let's use the slope formula to calculate the slope of the line through (-1,-17) and (3,11)

$(x_1,y_1) = (-1,-17) \text{ and } (x_2,y_2) = (3,11)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{11 - (-17)}{3 - (-1)}\\\\m = \frac{11 + 17}{3 + 1}\\\\m = \frac{28}{4}\\\\m = 7\\\\$

The slope of line A is 7

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Now let's find the slope of line B.

$(x_1,y_1) = (0,4) \text{ and } (x_2,y_2) = (7,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - 4}{7 - 0}\\\\m = -\frac{9}{7}\\\\$

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Now onto line C.

$(x_1,y_1) = (7,1) \text{ and } (x_2,y_2) = (0,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 1}{0 - 7}\\\\m = \frac{1}{-7}\\\\m = -\frac{1}{7}\\\\$

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Lastly we have line D.

$(x_1,y_1) = (-1,-6) \text{ and } (x_2,y_2) = (1,8)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{8 - (-6)}{1 - (-1)}\\\\m = \frac{8 + 6}{1 + 1}\\\\m = \frac{14}{2}\\\\m = 7\\\\$

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Here's a summary of the slopes we found

$\begin{array}{|c|c|} \cline{1-2}\text{Line} & \text{Slope}\\\cline{1-2}\text{A} & 7\\\cline{1-2}\text{B} & -9/7\\\cline{1-2}\text{C} & -1/7\\\cline{1-2}\text{D} & 7\\\cline{1-2}\end{array}$

Recall that parallel lines have equal slopes, but different y intercepts. This fact makes Line A parallel to line D.

Lines A and C are perpendicular to one another, because the slopes 7 and -1/7 multiply to -1. In other words, -1/7 is the negative reciprocal of 7, and vice versa. These two lines form a 90 degree angle.

Lines C and D are perpendicular for the same reasoning as the previous paragraph.

Line B unfortunately is neither parallel nor perpendicular to any of the other lines mentioned.

You can use a graphing tool like Desmos or GeoGebra to verify these answers.

6 0

11 months ago

Find the 7th term of the number pattern of general term 5n-4

olchik [2.2K]

Answer:

Step-by-step explanation:

n = 7 so it is:

5(7) - 4

= 35 - 4

= 31.

4 0

2 years ago

Please help if you could

Goshia [24]

Answer:

f(x)= 6x+9....

Step-by-step explanation:

The given equation is:

y-6x-9=0

Add 6x+9 at both sides:

y-6x-9+6x+9=0+6x+9

Solve the like terms:

on the L.H.S -6x will be cancelled out by +6x and -9 will be cancelled out by +9

y=6x+9

Now convert it in function notation:

f(x)=y

f(x)= 6x+9....

3 0

2 years ago

21 - 3 + 18 ÷ 6 =<br> 7 x 9 - 3 x 4 + 10 =

Igoryamba

Answer:

21 - 3 + 18 ÷ 6 = 21

7 x 9 - 3 x 4 + 10 = 61

Step-by-step explanation:

3 0

2 years ago

What is the product? (5r + 2)(3r − 4)

Novay_Z [31]

15r^2 - 14r -12 is the correct answer

8 0

3 years ago

Read 2 more answers