Answer:
To find the slope of line AB, we use the slope formula:
slope of AB = (yB - yA) / (xB - xA)
where A = (-10, 8) and B = (2, 3).
slope of AB = (3 - 8) / (2 - (-10)) = -5/12
The slope of a line perpendicular to AB will have a negative reciprocal slope, so its slope will be 12/5.
Using the slope-intercept form of the equation of a line:
y = mx + b
where m is the slope and b is the y-intercept, we can find the equation of the line that passes through point X (-5, 10) and has a slope of 12/5.
10 = (12/5)(-5) + b
10 = -24/5 + b
b = 74/5
Therefore, the equation of the line that is perpendicular to AB and passes through point X is:
y = (12/5)x + 74/5