Will the ineqaulity symbol change its direction when you subtract 5 from both sides?
2 answers:
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Answer: The answer is (D) Reflection across the line y = -x.
Step-by-step explanation: In figure given in the question, we can see two triangles, ΔABC and ΔA'B'C' where the second triangle is the result of transformation from the first one.
(A) If we rotate ΔABC 180° counterclockwise about the origin, then the image will coincide with ΔA'B'C'. So, this transformation can take place here.
(B) If we reflect ΔABC across the origin, then also the image will coincide with ΔA'B'C' and so this transformation can also take place.
(C) If we rotate ΔABC through 180° clockwise about the origin, the we will see the image will be same as ΔA'B'C'. Hence, this transformation can also take place.
(D) Finally, if we reflect ΔABC across the line y = -x, the the image formed will be different from ΔA'B'C', in fact, it is ΔA'D'E', as shown in the attached figure. So, this transformation can not take place here.
Thus, the correct option is (D).
Answer:
The lines are parallel, with the same slope of 5.
Step-by-step explanation:
Remember that if slopes are the same, then the lines are parallel. If the slopes are opposite reciprocals, they are perpendicular. If they are neither of those cases, then they would be neither.
1) Since y = 5x + 1 is already in slope-intercept format (y = mx + b, in which m represents the slope) we know that 5 is the slope of that equation.
2) To find the slope of -5x + y = 6, let's just convert it to the slope-intercept format by isolating y on the left side like so:
(All you need to do is move -5x to the right side of the equation.) So, by looking at y = 5x + 6, we can do the same thing we did from step 1 and find that the slope is 5.
3) Since both of the equations' slopes are 5, they share the same slope - therefore, they are parallel.
Hope this helps! Please do not hesitate to ask any questions.