Question

Ma poate ajuta cineva la acesta problema: pe o drepta g considerati punctele D, R,P si T coliniare in aceasta ordine astfel incat DR=PT=3 cm, iar RP=4cm

Answer 1

Givens

`DR=PT=3cm` and
`RP=4cm`

Points D, R, P and T are collinear.

The image attached shows a representation of this problem.

By sum of segments, we have

`DT=DR+RP+PT`

Replacing all given values, we have

`DT=3+4+3=10 \ cm`

Therefore, the segment DT is 10 centimeters long.

Now, we know that point E is the center of segment RP, which means is a middle point, divides the segment equally. So, to prove that segment DT is symmetrical regarding point E, we need to prove that both sides are equal.

`RE=EP=2cm`, by definition of middle point.

By sum of segments, we have

`DR+RE=3+2=5cm\\EP+PT=5cm`

Which means
`DR+RE=(DT)/(2)\\ EP+PT=(DT)/(2)`.

Therefore, segment DT is symmetrical regarding point E.