What set of reflections would carry triangle ABC onto itself?
2 answers:
You might be interested in
Let's put this on the usual Cartesian grid just so we can talk about it without drawing a picture. We'll use map conventions, right is east, up is north.
The ball starts at (0,0). 10.3 feet northwest means we have an isosceles right triangle whose diagonal is 10.3 feet. It's isosceles because northwest means equal parts north and west.
The sides of these triangles are in ratio
The negative sign indicates west, which doesn't really matter for this problem. The distance from the origin to this point is 10.3 as required.
Now a second putt of 3.8 feet north puts us at
The squared distance to the origin is exactly
A little calculator work tells us
Third choice.
Answer:
<u>Given expression:</u>
<u>The first root is valid when:</u>
- 2x + 2 ≥ 0 ⇒ 2x ≥ - 2 ⇒ x ≥ - 1
<u>The second root is valid when:</u>
- 6 - 4x ≥ 0 ⇒ 4x ≤ 6 ⇒ x ≤ 1.5
<u>So the variable x can get values within interval:</u>
- -1 ≤ x ≤ 1.5 or
- x = [-1, 1.5]