Answer:
A 180-degree clockwise rotation about the origin followed by a translation 1 unit to the left.
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
so the coordinates after the first putt are
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.
Step-by-step explanation:
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The distance formula measures the length of a line segment or the distance between two points.
The hypotenuse is one of the two sides that forms the right angle of a triangle.
The altitude of a triangle is a line segment that extends from the vertex and is perpendicular to the side opposite the vertex.