Answer is B. Zero
Reason
Pick any points on that line, they will have the same y value , it means they lie on a horizontal line. The slope of such a line is 0.
We are given that:
The skateboard park is located at the point (-3,5),
the ice cream shop is located at the point (-3,6),
and the comic book store is located at (4,6).
We are also given that the four coordinates forms a rectangle.
Here we already have two matching x- coordinates as -3 and y coordinates as 6.
Now we must have two matching x and y coordinates too.
As shown in figure , if we have the last coordinate as (4,5), it will complete the rectangle.
So answer is option B) (4,5) is the last coordinate at which his best friend lives.
The slope is -2.5 because you subtract 2y from both sides, then add two to both sides, then divide both sides by 2 to isolate y
Separate the vectors into their <em>x</em>- and <em>y</em>-components. Let <em>u</em> be the vector on the right and <em>v</em> the vector on the left, so that
<em>u</em> = 4 cos(45°) <em>x</em> + 4 sin(45°) <em>y</em>
<em>v</em> = 2 cos(135°) <em>x</em> + 2 sin(135°) <em>y</em>
where <em>x</em> and <em>y</em> denote the unit vectors in the <em>x</em> and <em>y</em> directions.
Then the sum is
<em>u</em> + <em>v</em> = (4 cos(45°) + 2 cos(135°)) <em>x</em> + (4 sin(45°) + 2 sin(135°)) <em>y</em>
and its magnitude is
||<em>u</em> + <em>v</em>|| = √((4 cos(45°) + 2 cos(135°))² + (4 sin(45°) + 2 sin(135°))²)
… = √(16 cos²(45°) + 16 cos(45°) cos(135°) + 4 cos²(135°) + 16 sin²(45°) + 16 sin(45°) sin(135°) + 4 sin²(135°))
… = √(16 (cos²(45°) + sin²(45°)) + 16 (cos(45°) cos(135°) + sin(45°) sin(135°)) + 4 (cos²(135°) + sin²(135°)))
… = √(16 + 16 cos(135° - 45°) + 4)
… = √(20 + 16 cos(90°))
… = √20 = 2√5
