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Answer:
y = ¹⁴/₄.x
Step-by-step explanation:
First of, if the bisector is perpendicular to the line segment, then we can find the gradient of the bisector () using the rule/principle:
Let:
m = gradient of the line segment
Then:
=
We can find m since we have two points that fall on the line segment, (5, -9) and (-9, -5):
Δy/Δx
We can now find :
The equation of a line can be found using:
y - y₁ = m(x - x₁)
We have the gradient of the perpendicular bisector, the only other thing we need to identify the equation of the bisector is coordinates of a point that fall on the line;
We know the line will pass through the point exactly midway between (5, -9) and (-9, -5) since it is a bisector;
This can be found by:
We have a point on the line and the gradient so we can now find the equation: