Mathematics, 16.11.2020 22:50 Destinywall

Are AB and CD parallel, perpendicular, or neither?*
1. A(-4, 8), B(4, 10), C(1, 1), D(-2, 13)

Answers: 2

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Answer from: chikooo

Perpendicular

Step-by-step explanation:

Given

A = (-4, 8)

B = (4, 10)

C = (1, 1)

D = (-2, 13)

Required

Is AB and CD parallel?

First, we need to calculate the slope (m) of AB and CD

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

For AB:

A (x_1,y_1)= (-4, 8)

B(x_2,y_2) = (4, 10)

So:

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

$m = \frac{10 - 8}{4 - (-4)}$

$m = \frac{10 - 8}{4 +4}$

$m = \frac{2}{8}$

$m = \frac{1}{4}$

For CD:

C(x_1,y_1) = (1, 1)

D(x_2,y_2) = (-2, 13)

So:

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

$m = \frac{13 - 1}{-2 - 1}$

$m = \frac{12}{-3}$

m = -4

For Lines to be parallel, the slope must be equal:

i.e. m_1 = m_2

This condition is not true because:

$\frac{1}{4} \neq -4$

For Lines to be perpendicular, the slope must be:

$m_1 = -\frac{1}{m_2}$

This implies:

$\frac{1}{4} = -\frac{1}{-4}$

$\frac{1}{4} = \frac{-1}{-4}$

$\frac{1}{4} = \frac{1}{4}$

Hence, the lines are perpendicular

Answer from: Quest

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

Me if you can and if you finished this lesson on edg- comment you.

Answer from: Quest

the correct answer is b. negative exponential growth.

step-by-step explanation:

you can tell it's an exponential function because it decreases rapidly then levels out and never touches the x-axis.

it is negative because the y-axis decreases as the x-axis increases.

therefore it is a negative exponential growth graph.

hope i !

Categorize the graph as linear increasing, linear decreasing, exponential growth, or negative expone

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Are AB and CD parallel, perpendicular, or neither?*
1. A(-4, 8), B(4, 10), C(1, 1), D(-2, 13)...

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