Question

Which transformations of quadrilateral PQRS would result in the image of the quadrilateral being located only in the first quadrant of the coordinate plane?

Select each correct answer.

A. a translation right 4 units
B. a reflection across x = 4
C. a reflection across y = −x
D. a rotation of 90˚ counterclockwise about vertex Q
E. a reflection across x=3, then a translation up 8 units
F. a reflection across the x-axis, then a translation up 13 units

Answer 1

Answer:

E

Step-by-step explanation:

The first quadrant is the top-right one

If a point is in the first quadrant, the x- and y-values of the point are both positive

Let's go through the one by one.

A) Translating the quadrilateral right 4 units will make the new S to be $(-3+4, -7)=(1, -7)$, which is not in the first quadrant.

B) Reflection the quadrilateral across $x=4$ will not change the y-value of any points. So, the new S will stay below the x-axis, and thus will never be in the first quadrant, because it will always have a negative y-value.

C) This one is tricky. We can prove(the proof is just taking cases of which quadrant) that if a point is in the second or fourth quadrant, it's reflection across the line $y=-x$ will always be in the same quadrant it started in(i.e. reflect a point in the second quadrant, you get a point in the second quadrant). We know that P is in the second quadrant, so the new P will also be in the second quadrant. Therefore, the new quadrilateral will not be entirely in the first quadrant.

D) We intuitively(and can prove) that because R is right underneath Q, the new R will be directly to the left of Q, with the same distance as Q to original R. So, the new R will be $(-10, 12)$ using above method. This point is not in the first quadrant.

E) We know intuitively(and can prove) that a reflection across the line $x=3$ will make the entire quadrilateral in the first and fourth quadrant. However, When we translate up, the new S, the lowest point on the quadrilateral, will be above the x-axis, making all the points in the first quadrant! Therefore, E works.

F) When we reflect across the x-axis, any points in the second quadrant go to the third quadrant. So, the new P will be in the third quadrant. However, when we translate up 13 units, the new P will go to the second quadrant. It will never cross the y-axis, and will always have a negative x-coordinate. Therefore, P will not be in the first quadrant.

Summing up the cases that work, we get that $\boxed{E}$ is the only answer.

Answer 2

The transformations of quadrilateral PQRS which would result in the image of the quadrilateral being located only in the first quadrant of the coordinate plane is:

• E. A reflection across x=3, then a translation up 8 units

What is a Quadrant?

This refers to the axis of a two dimensional Cartesian system which is one side out of four quarters of a circle or given shape.

From the given image, we can see that the first quadrant is at the top.

With this, we can see that the transformation which would make the quadrilateral PQRS to be in the first quadrant is a reflection across x=3, then a translation up 8 units.

This is because when we translate up, then we can see that the x-y values of the point are positive and which would make the translation up 8 points.

Read more about coordinate plane here:

https://brainly.com/question/18168162