Which Quadrant will triangle LAW be in when it is reflected across the y-axis and then reflected across the x-axis?

Triangle LOW
Point L: (-5, -2)
Point O: (-2, -4)
Point W: (-4, -6)

A. Quadrant III
B. Quadrant II
C. Quadrant IV
D. Quadrant I

1 answer

To find out which quadrant triangle LAW will be in after the specified reflections, we need to perform the reflections step by step on each point of the triangle.

  1. Reflection across the y-axis: When a point \((x, y)\) is reflected across the y-axis, its new coordinates become \((-x, y)\).

    • Point L: from \((-5, -2)\) to \((5, -2)\)
    • Point O: from \((-2, -4)\) to \((2, -4)\)
    • Point W: from \((-4, -6)\) to \((4, -6)\)

    After reflecting across the y-axis, the points are:

    • L: \((5, -2)\)
    • O: \((2, -4)\)
    • W: \((4, -6)\)
  2. Reflection across the x-axis: Next, when a point \((x, y)\) is reflected across the x-axis, its new coordinates become \((x, -y)\).

    • Point L: from \((5, -2)\) to \((5, 2)\)
    • Point O: from \((2, -4)\) to \((2, 4)\)
    • Point W: from \((4, -6)\) to \((4, 6)\)

    After reflecting across the x-axis, the points are:

    • L: \((5, 2)\)
    • O: \((2, 4)\)
    • W: \((4, 6)\)

Now let's determine the quadrant for each point:

  • Point L: \((5, 2)\) is in Quadrant I (x > 0, y > 0)
  • Point O: \((2, 4)\) is in Quadrant I (x > 0, y > 0)
  • Point W: \((4, 6)\) is in Quadrant I (x > 0, y > 0)

All the points of triangle LAW after both reflections are in Quadrant I. Thus, the answer is:

D. Quadrant I