Question

Triangle ABC is graphed on a coordinate grid so that A is (5,5), B is (0,-3), and C is (-3,11). The triangle is reflected across the y-axis to create triangle XBY where angle A corresponds to angle X. What is the length of XY?

Option 1: 5 units
Option 2: 8 units
Option 3: 10 units
Option 4: 16 units

Answer 1

The length of line segment XY after reflecting point A across the y-axis to point X is 10 units.

Step-by-step explanation:

Since triangle ABC is reflected across the y-axis, point A at (5,5) will be reflected to point X at (-5,5). The coordinates of X are obtained by changing the sign of the x-coordinate of A while keeping the y-coordinate the same. The distance between points A and X, defined as XY, can be calculated using the distance formula or by recognizing they lay horizontally apart on the grid.

To find the length of XY, you simply look at the difference in the x-coordinates of A and X because they share the same y-coordinate:

Length of XY = |x2 - x1| = |-5 - 5| = 10 units.