Question

The point (7,8) in the coordinate plane represents a ratio. adela claims that you can find equivalent ratio by adding the same number to both coordinate of the point. is adela correct? explain.

Answer 1

No, adding the same number to both coordinates of a point does not result in an equivalent ratio.

Step-by-step explanation:

No, Adela is not correct. Adding the same number to both coordinates of a point does not result in an equivalent ratio. The coordinates of a point represent the x and y coordinates on a coordinate plane. A ratio, on the other hand, compares two quantities. Adding the same number to both coordinates simply shifts the point on the coordinate plane, but it does not change the ratio it represents.

Thus, Adela is not correct in claiming that you can find an equivalent ratio by adding the same number to both coordinates of the point. An equivalent ratio is found when both terms of the ratio are multiplied or divided by the same non-zero number, maintaining the same proportion. The correct way to find equivalent ratios is to maintain the proportional relationship, which means applying the same scale factor to both terms of the ratio.

Answer 2

Adela is incorrect; equivalent ratios are found by multiplying (or dividing) both terms by the same number to maintain the same proportion. Adding the same number alters the ratio instead of preserving its proportionality.

Step-by-step explanation:

Adela is not correct in claiming that you can find an equivalent ratio by adding the same number to both coordinates of the point. An equivalent ratio is found when both terms of the ratio are multiplied or divided by the same non-zero number, maintaining the same proportion.

To illustrate this with an example, if we have the ratio represented by the point (7,8), and we multiply both terms by 2, we get an equivalent ratio (14,16), which simplifies to (7,8). However, if we were to add 2 to both coordinates, we would get (9,10), which is not the same ratio, as 9/10 does not simplify to 7/8.

The correct way to find equivalent ratios is to maintain the proportional relationship, which means applying the same scale factor to both terms of the ratio. In terms of coordinate planes and graphs, ratios represented by points on the same line passing through the origin (0,0) will be equivalent as they have the same slope which also represents their scale factor.