Question

Angle MNO is formed by segments MN and NO on the following coordinate grid:

A coordinate grid is shown from positive 6 to negative 6 on the x axis and from positive 6 to negative 6 on the y axis. A line segment MN is shown with M as ordered pair negative 1, 1 and N as ordered pair negative 5, 4. Another line segment NO is shown with O as ordered pair negative 1, 4.

Angle MNO is rotated 90 degrees counterclockwise about the origin to form angle M′N′O′. Which statement shows the measure of angle M′N′O′?

m∠ M′N′O′ = 90 degrees
m∠ M′N′O′ = 180 degrees
m∠ M′N′O′ = 2 ⋅ m∠MNO
m∠ M′N′O′ = m∠MNO

Answer 1

Answer:

I am 90% sure that the answer is M'N'O' is 90*

Step-by-step explanation:

A line segment MN is shown as M = -1,1 and N= -5,4 this makes a diagonal line across the grid. Another line segment NO is shown with O as ordered pair negative 1, 4. Angle MNO is rotated 90 degrees counterclockwise about the origin to form angle M′N′O′. this is where the angles meet, Rotating the shape (or the angles) does not change the degree of the angle of the shape. I am 99% sure that an 90* angle would be formed. but im just in middle school so what do i know?

Answer 2

Answer with explanation:

It is given that ,∠M NO is formed by segments MN and NO on the following coordinate grid.

Coordinate of Point M = (-1,1)

Coordinate of Point N= (-5,4)

Coordinate of Point O= (-1,4)

$MN=\sqrt{(-1+5)^2+(1-4)^2}\\\\MN=\sqrt{16+9}\\\\MN=5\\\\NO=\sqrt{(-1+5)^2+(4-4)^2}\\\\NO=4\\\\MO=\sqrt{(-1+1)^2+(4-1)^2}\\\\MO=3$

MO²+NO²=MN²

So,By Pythagorean Theorem, ΔM NO is right Angled Triangle having ∠ O=90°.

Now, it is given that, ∠MNO is rotated 90 degrees counterclockwise about the origin to form ∠ M′N′O′.

⇒When we rotate a Triangle either Anticlockwise or Clockwise the triangle before Rotation and Triangle after rotation will be congruent to each other.

Option D:→

 m∠ M′N′O′ = m∠M NO