The path of a race will be drawn on a coordinate grid like the one shown below. The starting point of the race will be at (−5.4, 3). The finishing point will be at (3, −5.4). A four-quadrant coordinate grid is drawn from negative 4 to positive 4. Quadrant I is labeled Quadrant P, Quadrant II is labeled Quadrant Q, Quadrant III is labeled Quadrant R, and Quadrant IV is labeled Quadrant S.

Part A: Use the grid to determine in which quadrants the starting point and the finishing point are located. Explain how you determined the locations. (6 points)

Part B: A checkpoint will be at (5.4, 3). In at least two sentences, describe the difference between the coordinates of the starting point and the checkpoint, and explain how the points are related. (4 points)

(-5.4,3) is in the IInd quadrant, (3,-5.4) is in the IVth quadrant.

Mirror image of (-5.4,3)

Step-by-step explanation:

(a) The points are (-5.4,3) and (3,-5.4).

The origin is the center point of the graph. The right side of the x axis is positive the left side is negative. The upward direction from the origin is the positive y axis and the downward direction is negative y axis.

For (-5.4,3) the x axis location is -5.4 and the y axis location is 3

For (3,-5.4) the x axis location is 3 and the y axis location is -5.4

So, the point (-5.4,3) is in the IInd quadrant and the point (3,-5.4) is in the IVth quadrant.

(b) A mirror image with respect to y axis is the point on the opposite side of the quadrant where the point on x axis has changed the sign and y axis point remains constant.

The point (5.4,3) is the mirror image of the point (-5.4,3) with respect to y axis.

The point (3,-5.4) has the x and y points interchanged and the sign of the point on the y axis has changed when comparing to (5.4,3).

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.