Final answer:
To find the ratio in which point (3, 3) divides the line joining A(7, 1) and B(1, 4), we can use the concept of section formula. The ratio is approximately 4.5:3.2.
Step-by-step explanation:
To find the ratio in which point (3, 3) divides the line joining A(7, 1) and B(1, 4), we can use the concept of section formula. The section formula states that a point dividing a line segment in a ratio of m:n internally has coordinates given by:
x = (mx₁ + nx₂) / (m + n)
y = (my₁ + ny₂) / (m + n)
Using this formula, we can substitute the given values:
x = (3 * 7 + 1 * 1) / (3 + 1) = 5
y = (3 * 1 + 1 * 4) / (3 + 1) = 7/2
Therefore, the coordinates of the point where (3, 3) divides the line AB are (5, 7/2). To find the ratio, we can compare the distances of the point from the two given points.
AB = sqrt((7 - 1)² + (1 - 4)²) = sqrt(36) = 6
AP = sqrt((5 - 1)² + (7/2 - 4)²) = sqrt(20.25) = 4.5
PB = sqrt((7 - 5)² + (1 - 7/2)²) = sqrt(10.25) = 3.2
Since AP:PB is approximately 4.5:3.2, the ratio in which point (3, 3) divides the line AB is approximately 4.5:3.2.