Parallelogram abcd is reflected over the y axis, followed by a reflection over the x axis, and then rotated 180 degrees about the origin,. what is the location of point a after the transformations are complete? a (-5,-1) b. (5,1) ,1) d.(5,-1)

Option c.

Step-by-step explanation:

The missing figure is attached.

Given a point :

1. If it is reflected over the y-axis:

→

2. If it is reflected over the x-axis:

→

3. If it is rotated 180 degrees about the origin:

→

In this case, you can identify that the point A is:

Then:

If it is reflected over the y-axis:

→

If then it is reflected over the x-axis:

→

Finally, if this is followed by a rotationf of 180 degrees about the origin, this is:

→

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12