A coordinate plane showing 4 quadrants has two triangles plotted on it. Triangle upper C upper B upper A is plotted in quadrant 2, and triangle upper J upper K upper L is plotted in quadrants 1 and 4.

Question

Which sequence of rigid motions would map △CBA
onto △JKL
?

(1 point)
Responses

translation along the vector mapping point C
to point J
, followed by a reflection across JK¯¯¯¯¯¯¯¯
translation along the vector mapping point upper C to point upper J , followed by a reflection across Modifying above upper J upper K with bar

rotation −180°
(clockwise) about the origin
rotation negative 180 degrees (clockwise) about the origin

reflection across the line x=0
reflection across the line x equals 0

reflection across the y-axis, then translation along the vector mapping point C
to point K

Answer 1

To map triangle \( CBA \) in quadrant 2 onto triangle \( JKL \) in quadrants 1 and 4, we need to consider the relative positions and orientations of the triangles.

1. Understanding the positions:

   • Triangle \( CBA \) is in quadrant 2, where the x-coordinates are negative and y-coordinates are positive.
   • Triangle \( JKL \) extends into both quadrant 1 (where both x and y are positive) and quadrant 4 (where x is positive and y is negative).

2. Mapping Strategy:

   • The most straightforward way to map a triangle from quadrant 2 to quadrant 1 involves reflecting across the y-axis (which takes the triangle from quadrant 2 to quadrant 1) and then translating it to align with \( JKL \).

3. Choices Breakdown:

   • The first option involves translating along the vector mapping point \( C \) to point \( J \), followed by a reflection across line \( \overline{JK} \). This could potentially work, but it depends on the specifics of the triangle placements – we need more information about the coordinates.
   • The rotation of 180 degrees clockwise about the origin would map quadrant 2 to quadrant 4, which wouldn't be conducive for mapping \( CBA \) to \( JKL \).
   • The reflection across the line \( x = 0 \) is equivalent to reflecting across the y-axis.
   • The reflection across the y-axis, then translation along the vector mapping point \( C \) to point \( K \) could effectively reposition the triangle as well, particularly if \( K \) is aligned with \( A \).

Given all of this, the most direct answer involves reflecting across the y-axis first to move the triangle into the correct quadrant and position, followed by a translation if necessary.

Therefore, the best choice is:

reflection across the y-axis, then translation along the vector mapping point C to point K.