Answer:
EG = 19
Step-by-step explanation:
* Lets explain how to solve the problem
- If a line bisects another line that means the point of intersection
divides the second line into two equal parts
∵ EF bisects CD at G
∴ CG = GD
∵ CG = 5x - 1
∵ GD = 7x - 13
∴ 7x - 13 = 5x - 1
* Lets solve the equation
∵ 7x - 13 = 5x - 1
- Subtract 5x from both sides and add 13 to both sides
∴ 7x - 5x = 13 - 1
∴ 2x = 12
- Divide both sides by 2
∴ x = 6
- Point G divides EF into two parts EG and GF
∴ EF = EG + GF
∵ EF = 6x - 4
- Substitute the value of x to find EF
∵ x = 6
∴ EF = 6(6) - 4 = 36 - 4 = 32
∴ EF = 32
∵ GF = 13
- Substitute the values of EF and GF in the equation of EF
∴ 32 = EG + 13
- Subtract 13 from both sides
∴ 19 = EG
* EG = 19
The point such that the coordinate is 5;3 is (14, 0)
<h3>Midpoint of coordinates using ratio</h3>
The formula for finding the midpoint of a line in the ratio m:n is expressed as:
M(x, y) = {(mx₁+nx₂)/2, (my₁+ny₂)/2,}
Given the coordinate of G and D on the line as G(5, 0) and D(1,0)
Since there is no y-axis, hence;
x = 5(5)+1(3)/2
x = 25+3/2
x = 28/2
x =14
Hence the point such that the ratio is 5;3 is (14, 0)
Learn more on midpoint of a line here: brainly.com/question/5566419
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