Triangle ABC and triangle CDE are similar right triangles. Which proportion can be used to show that the slope of AC is equal to the slope of CE?%0D%0AResponses%0D%0A%0D%0A%0D%0AA%093−5−4−0%0D%0A3%0D%0A−%0D%0A5%0D%0A−%0D%0A4%0D%0A−%0D%0A0%0D%0A = 3−20−2%0D%0A3%0D%0A−%0D%0A2%0D%0A0%0D%0A−%0D%0A2%0D%0A3 − 5 − 4 − 0 = 3 − 2 0 − 2%0D%0A%0D%0A%0D%0AB%093−5−4−0%0D%0A3%0D%0A−%0D%0A5%0D%0A−%0D%0A4%0D%0A−%0D%0A0%0D%0A = 3−22−0%0D%0A3%0D%0A−%0D%0A2%0D%0A2%0D%0A−%0D%0A0%0D%0A3 − 5 − 4 − 0 = 3 − 2 2 − 0%0D%0A%0D%0A%0D%0AC%095−3−4−0%0D%0A5%0D%0A−%0D%0A3%0D%0A−%0D%0A4%0D%0A−%0D%0A0%0D%0A = 3−20−2%0D%0A3%0D%0A−%0D%0A2%0D%0A0%0D%0A−%0D%0A2%0D%0A5 − 3 − 4 − 0 = 3 − 2 0 − 2%0D%0A%0D%0A%0D%0AD%095−3−4−0%0D%0A5%0D%0A−%0D%0A3%0D%0A−%0D%0A4%0D%0A−%0D%0A0%0D%0A = 2−30−2

Question

Triangle ABC and triangle CDE are similar right triangles. Which proportion can be used to show that the slope of AC is equal to the slope of CE?%0D%0AResponses%0D%0A%0D%0A%0D%0AA%093−5−4−0%0D%0A3%0D%0A−%0D%0A5%0D%0A−%0D%0A4%0D%0A−%0D%0A0%0D%0A = 3−20−2%0D%0A3%0D%0A−%0D%0A2%0D%0A0%0D%0A−%0D%0A2%0D%0A3 − 5 − 4 − 0 = 3 − 2 0 − 2%0D%0A%0D%0A%0D%0AB%093−5−4−0%0D%0A3%0D%0A−%0D%0A5%0D%0A−%0D%0A4%0D%0A−%0D%0A0%0D%0A = 3−22−0%0D%0A3%0D%0A−%0D%0A2%0D%0A2%0D%0A−%0D%0A0%0D%0A3 − 5 − 4 − 0 = 3 − 2 2 − 0%0D%0A%0D%0A%0D%0AC%095−3−4−0%0D%0A5%0D%0A−%0D%0A3%0D%0A−%0D%0A4%0D%0A−%0D%0A0%0D%0A = 3−20−2%0D%0A3%0D%0A−%0D%0A2%0D%0A0%0D%0A−%0D%0A2%0D%0A5 − 3 − 4 − 0 = 3 − 2 0 − 2%0D%0A%0D%0A%0D%0AD%095−3−4−0%0D%0A5%0D%0A−%0D%0A3%0D%0A−%0D%0A4%0D%0A−%0D%0A0%0D%0A = 2−30−2

Answer 1

The proportion that can be used to show that the slope of AC is equal to the slope of CE is:

AC/CE = (3-5)/(3-2) = (-2)/(-2)

So the correct option is:

D) 3-5-4-0 = 2-3-0-2

Answer 2

To show that the slope of AC is equal to the slope of CE, we can use the proportion of the corresponding side lengths of the two triangles.

First, let's label the points of the triangles:

Triangle ABC:
A = (3, -5)
B = (-4, 0)
C = (3, -2)

Triangle CDE:
C = (3, -2)
D = (5, -3)
E = (4, 0)

Now, let's calculate the slope of AC:

slope of AC = (change in y-coordinates)/(change in x-coordinates)
= (-2 - (-5))/(3 - 3)
= 3/0

We have a zero in the denominator, which means that the slope of AC is undefined.

Next, let's calculate the slope of CE:

slope of CE = (change in y-coordinates)/(change in x-coordinates)
= (0 - (-2))/(4 - 3)
= 2/1
= 2

Now, let's compare the slopes:

The slope of AC is undefined, and the slope of CE is 2. Since undefined is not equal to 2, we cannot use a proportion to show that the slope of AC is equal to the slope of CE.

Therefore, the correct response is: None of the given proportions can be used to show that the slope of AC is equal to the slope of CE.

Answer 3

To show that the slope of AC is equal to the slope of CE, we can use the proportion involving the coordinates of the two points.

The proportion is:

(BC - BA) / (EC - EA) = (AC - AE) / (DC - DA)

Let's substitute the given values into the proportion:

(3 - 5) / (-4 - 0) = (3 - 2) / (0 - 2)

Simplifying the expression on the left side:

-2 / -4 = 1 / -2

Both sides of the equation simplify to 1/2.

Therefore, we can conclude that the slope of AC is equal to the slope of CE.