Answer :
Answer:
Find the slope of the line AB:
The slope (m) of the line joining A (1, 0) and B (2, 3) is:
m = (y2 - y1) / (x2 - x1) = (3 - 0) / (2 - 1) = 3 / 1 = 3
Since the perpendicular line is internal, use section formula:
Let C be the point of division in the ratio 1:5. We can use the section formula to find its coordinates:
x_C = (1 * 2 + 5 * 1) / (1 + 5) = 7 / 6
y_C = (1 * 3 + 5 * 0) / (1 + 5) = 3 / 6 = 1/2
Perpendicular lines have negative reciprocals of each other's slopes:
The slope of the perpendicular line (m') will be the negative reciprocal of m:
m' = -1 / m = -1 / 3
Use the point-slope form to find the equation of the perpendicular line:
We have the slope (m') and a point C (x_C, y_C). Now we can use the point-slope form of linear equations:
y - y_C = m' (x - x_C)
Substitute the values:
y - (1/2) = (-1/3) (x - (7/6))
Simplify the equation:
y = (-1/3)x + (5/6) + (1/2)
y = (-1/3)x + 7/12
Therefore, the equation of the line perpendicular to line segment AB, dividing it internally at a ratio of 1:5, is:
y = (-1/3)x + 7/12
Step-by-step explanation:
already explained