Points M, P and O belong to the same straight line, and points M and P lie on different sides from point O.

| January 12, 2021 | education

Points M, P and O belong to the same straight line, and points M and P lie on different sides from point O. Find the lengths of the segments OM and OP if MP = 28cm, and the segment OM is 12cm shorter than the segment OP.

We solve this problem using the equation, for this we use the corresponding expressions for these segments.
Considering that the MO segment is 12 cm shorter than the PO segment and the MР = 28 cm segment, we have:
let the segment MO = x, and PO = x + 12, make up the equation,
x + (x + 12) = 28;
2x + 12 = 28;
We transfer the known term of the equation from the left to the right, while changing the sign of the term to the opposite.
2x = 28 – 12;
2x = 16;
To find an unknown factor, the product must be divided by a known factor.
x = 8 is the root of the equation.
Hence MO = 8 (cm), PO = 8 + 12 = 20 (cm).
Answer: 8 cm, 20 cm.



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