Question

∆ ABC and ∆ CDE are similar right triangles. The coordinates of all the vertices are integers.

First-quadrant graph showing a ray through the origin and the points A, C, and E. Point A is 3 comma 2, point C is 9 comma 6, and point E is 12 comma 8. There are two right triangles. Triangle A B C has a right angle at point B. Triangle C D E has a right angle at point D. The coordinates of point B are 3 comma 6. The coordinates of point D are 9 comma 8.

Which statement below is correct?

A. The slope of AC is greater than the slope of CE. This is because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is greater for AC than for CE.

B. The relationship between the slope of AC and the slope of CE cannot be determined because the triangles are congruent.

C. The slope of AC is equal to the slope of CE. This is because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is the same for AC and CE.

D. The slope of AC is less than the slope of CE. This is because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is less for AC than for CE.

Answer 1

Answer: Not sure but try D

Step-by-step explanation:

not sure

Answer 2

The slope of a line is the change in y values divided by the change in x values.

The correct statement is:

C. The slope of AC is equal to the slope of CE. This is because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is the same for AC and CE.

The coordinates of $\triangle ABC$ are:

$A = (3,2)$

$B = (3,6)$

$C = (9,6)$

The coordinates of $\triangle CDE$ are:

$C = (9,6)$

$D =(9,8)$

$E = (12,8)$

$\triangle ABC$ is right-angled at B.

So, the slope will be calculated from points A and C

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

$m= \frac{6-2}{9-3}$

$m= \frac{4}{6}$

$m= \frac{2}{3}$

$\triangle CDE$ is right-angled at D.

So, the slope will be calculated from points C and E

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

$m= \frac{8 - 6}{12-9}$

$m= \frac{2}{3}$

The calculated slope of both triangles are equal (i.e. 2/3)

Hence, the correct option is (c)

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