Question

The points (a,b) and (c,d) form a segment, and the points (d,e) and (d,f) form a segment. Create an equation assuming the segments are congruent

Answer 1

If the segments are congurent they are of equal length.

So constructing an equation will not be hard.

Take for example $y=x$ and limit x to be between and including 0 and 1 for the first segment. In this case our segment is $(a,b)\to(c,d)=(0,0)\to(1,1)$.

Now, d has been fixated to the value of 1 and we need to construct a segment from $(1,e)\to(1,f)$.

Since both x coordinates of the endpoints of the segment are fixed to be 1, we cannot run anymore, that is, we fixated our run. But on the rise (y-axis direction) we can still move one unit up.

Let e be 1 and f be 2. The distance between $(1,1)$ and $(1,2)$ is 1 which is also the distance between $(0,0)$ and $(1,1)$.

Now we are asked to find the equation of both segments.

First segment is described by $y=x$ with limited domain of $0\leq x\leq1$.

Second segment is described by $x=2$ with again limited domain of $1\leq y\leq2$.

Hope this helps :)

Answer 2

The length, l of a segment with points (x₁, y₁), and (x₂, y₂) is presented as follows; $l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

An equation that can be created given that the segment with points (a, b) and (c, d), and the segment with points (d, e), and (d, f) are congruent is presented as follows;

√((d - b)² + (c - a)²) = f - e

The reason the above equation is correct is presented as follows;

Given that the segments are congruent, therefore;

Length of (a, b) and (c, d) = Length of (d, e) and (d, f)

Length of (a, b) and (c, d) = √((d - b)² + (c - a)²)

Length of (d, e) and (d, f) = √((f - e)² + (d - d)²) = f - e

Which gives the equation;

√((d - b)² + (c - a)²) = f - e

Learn more about segments in the coordinate plane here:

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