Point p is located in the first quadrant of a coordinate plane. If p is reflected across to form p',choose the four statements that will always be true.

When we do a reflection of a point (x, y) about a given line, the distance between the point (x, y) and the line is invariant under the transformation.

In the case of reflection over x-axis we have:

T (x, y) => (x, -y)

In the case of reflection over the y-axis, we have:

T (x, y) => (-x, y)

Because these two lines are perpendicular, a reflection over the x-axis leaves the distance between the point and the y-axis invariant (and the same for the inverse case)

Then 4 statements that will always be true:

1) The distance between p' and the x-axis is the same as the distance between p and the x-axis.

2) The distance between p' and the y-axis is the same as the distance between p and the y-axis.

From 1 and 2, we get:

3)  The distance between p' and the origin is the same as the distance between p and the origin.

4) As we have a reflection, p' can not be in the same quadrant than p, then p' can not lie on the first quadrant.

b

step-by-step explanation:

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.