Question

select all the true statements.
a. dilations always increase the length of line segments
b. dilations take perpendicular lines to perpendicular lines
c. dilations of an angle are congruent to the original angle.
d. dilations increase the measure of angles.
e. dilations of a triangle are congruent to the original triangle.
f. dilations of a triangle are similar to the original triangle
question: 8
triangle pqr is shown on the coordinate plane
triangle pqr is rotated 180° clockwise about the origin to form the image pqr triangle (not shown).
what are the signs of coordinates (x, y) of point r?
a. both x and y are positive.
b. x is negative and y is positive.
c. both x and y are negative.
d. x is positive and y is negative.

Explanation:

Step1: Recall rotation rule

When a point \((x,y)\) is rotated \(180^{\circ}\) clockwise about the origin, the new coordinates \((x',y')\) are given by \((x',y')=(-x,-y)\).

Step2: Find original coordinates of \(R\)

From the coordinate - plane, the coordinates of point \(R\) are \((2, - 1)\).

Step3: Apply the rotation rule

For \(x = 2\) and \(y=-1\), after a \(180^{\circ}\) clockwise rotation about the origin, \(x'=-2\) and \(y' = 1\).

Answer:

B. \(x\) is negative and \(y\) is positive.