Answer: 1.465 : 1
Explanation:
Slope of the line segment:
m = (5 - 3)/(4 - (-2)) = 2/6 = 1/3
The equation of the line which the line segment lies on is found by:
(y - 3)/(x - (-2)) = 1/3
(y - 3)/(x + 2) = 1/3
(y - 3)/(x + 2) * (x + 2) = 1/3 * (x + 2)
y - 3 = (x + 2)/3 = 1/3 x + 2/3
y = 1/3 x + 11/3
The equation of the line given:
4x + 5y = 21
5y = -4x + 21
y = -4/5 * x + 21/5
Set them equal to each other and solve for x to find their intersection:
1/3 x + 11/3 = -4/5 * x + 21/5
15(1/3 x + 11/3) = 15(-4/5 * x + 21/5)
5 x + 55 = -12 x + 63
17x = 8
x = 8/17
y = 1/3 (8/17) + 11/3 = 8/51 + 181/51 = 189/51
Point (8/17, 189/51)
Distance from right end of segment to intersection:
s = SQRT((4 - 8/17)^2 + (5 - 189/51)^2) = SQRT((60/17)^2 + (66/51)^2) = 3.759
length of segment = SQRT((5–3)^2 + (4 - (-2))^2) = SQRT(4 + 36) = SQRT(40) = 6.324
Distance from the left end to interseciton:
6.324 - 3.759 = 2.555
Ratio of right end to left end:
3.759/2.565 = 1.465