Question

the coordinates of the vertices of a quadrilateral are n (1,1), t (1, - 4), q (-2, -1), and z (-2, 4). the figure is rotated 180° clockwise with the origin as the center of rotation to create quadrilateral ntqz. what are the coordinates of the vertices of quadrilateral ntqz? n = t =

Explanation:

Step1: Recall rotation rule

When rotating a point $(x,y)$ 180° clockwise about the origin, the new - point is $(-x,-y)$.

Step2: Find coordinates of $N'$

For point $N(1,1)$, applying the rule: $x = 1,y = 1$, so $N'=(-1,-1)$.

Step3: Find coordinates of $T'$

For point $T(1, - 4)$, with $x = 1,y=-4$, then $T'=(-1,4)$.

Step4: Find coordinates of $Q'$

For point $Q(-2,-1)$, where $x=-2,y = - 1$, so $Q'=(2,1)$.

Step5: Find coordinates of $Z'$

For point $Z(-2,4)$, with $x=-2,y = 4$, then $Z'=(2,-4)$.

Answer:

$N'=(-1,-1)$
$T'=(-1,4)$
$Q'=(2,1)$
$Z'=(2,-4)$