The length of a segment is the number of units on the segment.
The ratio of line segment AC to line segment BC is 3 : 1
The coordinate points are given as:
[tex]\mathbf{A = (3,8)}[/tex]
[tex]\mathbf{B = (15,9)}[/tex]
[tex]\mathbf{C = (21,9.5)}[/tex]
The length of each segment will be calculated using the following distance formula
[tex]\mathbf{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}[/tex]
So, we have:
[tex]\mathbf{AC = \sqrt{(3 - 21)^2 + (8 - 9.5)^2}}[/tex]
[tex]\mathbf{AC = \sqrt{326.25}}[/tex]
Also, we have:
[tex]\mathbf{BC = \sqrt{(15 - 21)^2 + (9 - 9.5)^2}}[/tex]
[tex]\mathbf{BC = \sqrt{36.25}}[/tex]
The ratio of AC to BC is represented as:
[tex]\mathbf{AC : BC = \sqrt{326.25}:\sqrt{36.25}}[/tex]
Divide through by [tex]\sqrt{36.25[/tex]
[tex]\mathbf{AC : BC = \sqrt{9} : \sqrt{1}}[/tex]
Evaluate square roots
[tex]\mathbf{AC : BC = 3 : 1}[/tex]
Hence, the ratio is 3 to 1
Read more about line segments at:
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