Final answer:
In ΔXYZ, the slope of line XZ is -5/9, the slope of YZ is 2/7, and the slope of line XY is -7/2. The triangle is not a right triangle because none of the slopes are negative reciprocals of each other.
Step-by-step explanation:
To find the slope of the lines in triangle ΔXYZ with vertices X(-5, 5), Y(-3, -2), and Z(4, 0), we use the slope formula m = (y2 - y1) / (x2 - x1). For line XZ, we plug in the coordinates of X and Z into this formula. The slope of line XZ is m = (0 - 5) / (4 - (-5)) = -5 / 9.
Similarly, for line YZ, we use the coordinates of Y and Z. The slope of line YZ is m = (0 - (-2)) / (4 - (-3)) = 2 / 7.
Next, for line XY, we use the coordinates of X and Y. The slope of line XY is m = (-2 - 5) / (-3 - (-5)) = -7 / 2.
To see if ΔXYZ is a right triangle, you can check if any of the slopes are negative reciprocals of each other. However, none of the slopes calculated (-5/9, 2/7, -7/2) are negative reciprocals, meaning they do not form a right angle. Therefore, ΔXYZ is not a right triangle.