4. Point E is located at (–2, 2) and point F is located at (4, –6). What is the distance between points E and F?

a. square root of 52
b. square root of 28
c. 10
d. square root of 20

5. In which quadrant is the point (x, y) located if x is negative and y is positive?

a. II
b. III
c. IV
d. I

6. Point A(8, –10) is reflected over the y-axis. Write the coordinates of A'.

a. (–8, –10)
b. (8, 10)
c. (8, –10)
d. (–8, 10)

What choices did you make?

c

d
a

right answers

4.?
5. A
6. B

5 is c quadrant 4 quadrant 4 is bottom right or a negative x positive y

4. To find the distance between points E and F, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula states that the distance between two points (x1, y1) and (x2, y2) is given by the formula:

√((x2 - x1)^2 + (y2 - y1)^2)

In this case, point E is located at (-2, 2) and point F is located at (4, -6). Plugging these coordinates into the distance formula, we get:

√((4 - (-2))^2 + (-6 - 2)^2)
√((6)^2 + (-8)^2)
√(36 + 64)
√(100)
10

Therefore, the distance between points E and F is 10. So the correct answer is option c.

5. When x is negative and y is positive, the point (x, y) is located in the second quadrant (II). In the Cartesian coordinate system, the second quadrant is the area to the left of the y-axis and above the x-axis. So the correct answer is option a.

6. Reflecting a point over the y-axis negates the x-coordinate while keeping the y-coordinate the same. In this case, point A is located at (8, -10). Reflecting it over the y-axis gives us (-8, -10). Therefore, the coordinates of A' are (-8, -10). So the correct answer is option a.