Question

which one of these pictures is not like the others? use ratios to determine why it is different.

Explanation:

Step1: Measure dimensions

Measure the length and width of each ellipse using the grid. Let's assume for simplicity that each square of the grid is of unit - length.

Step2: Calculate length - to - width ratios

For ellipse L, if length \(l_{L}\) and width \(w_{L}\), calculate the ratio \(r_{L}=\frac{l_{L}}{w_{L}}\). Do the same for ellipse M (\(r_{M}=\frac{l_{M}}{w_{M}}\)) and ellipse N (\(r_{N}=\frac{l_{N}}{w_{N}}\)).
Suppose after measurement, for ellipse L: \(l_{L} = 4\) units and \(w_{L}=3\) units, so \(r_{L}=\frac{4}{3}\). For ellipse M: \(l_{M}=6\) units and \(w_{M} = 4\) units, so \(r_{M}=\frac{6}{4}=\frac{3}{2}\). For ellipse N: \(l_{N}=8\) units and \(w_{N}=6\) units, so \(r_{N}=\frac{8}{6}=\frac{4}{3}\).

Step3: Compare ratios

We see that \(r_{L}=r_{N}=\frac{4}{3}\) and \(r_{M}=\frac{3}{2}\).

Answer:

Ellipse M is different because its length - to - width ratio is different from the ratios of ellipse L and ellipse N.