Name 4 points that would form a square with the origin at is center.
1 answer:
9514 1404 393
Answer:
(2, 3), (-3, 2), (-2, -3), (3, -2)
Step-by-step explanation:
You can pick any point you like, then rotate it around the origin to the four quadrants (or axes) by the transformation ...
(x, y) ⇒ (-y, x) . . . . . . . . . 90° rotation CCW
That is a rotation 90° CCW. Of course a rotation CW can do the same thing for you.
__
One possible square is ...
(2, 3), (-3, 2), (-2, -3), (3, -2)
You might be interested in
I will be using a practice problem with different endpoints, and I challenge you to solve this one using a similar strategy. The points I will be using is
(1, 3) as T and (5, 4) as the midpoint
Alright - we know that the equation for the midpoint of a line segment is
Next, we plug the x values in - since the midpoint's x value is 5 and one endpoint's x value is 1, we have
.
Next, we multiply both sides by 2, resulting in 1+x₂=10. Lastly, we subtract 1 from both sides, meaning that x₂, or the x value of the other endpoint, is 9. For the y values, we use a similar process -
.
since 3 is the y value of one endpoint and 4 is the y value of the midpoint. Multiplying both sides by 2, we get 3+y₂=8. Subtracting 3 from both sides, we get y₂=5 and our coordinates for the other endpoint to be (9, 5).
Good luck, and feel free to ask any questions as necessary!
(1, 3) as T and (5, 4) as the midpoint
Alright - we know that the equation for the midpoint of a line segment is
Next, we plug the x values in - since the midpoint's x value is 5 and one endpoint's x value is 1, we have
Next, we multiply both sides by 2, resulting in 1+x₂=10. Lastly, we subtract 1 from both sides, meaning that x₂, or the x value of the other endpoint, is 9. For the y values, we use a similar process -
since 3 is the y value of one endpoint and 4 is the y value of the midpoint. Multiplying both sides by 2, we get 3+y₂=8. Subtracting 3 from both sides, we get y₂=5 and our coordinates for the other endpoint to be (9, 5).
Good luck, and feel free to ask any questions as necessary!
we know that
<u>The Side-Splitter Theorem</u>: States that If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those two sides proportionally
so
in this problem
therefore
<u>the answer is</u>
The segment length is GJ