Answer:
The Marginal Rate of Substitution (MRS) is defined as the amount of good that a consumer is ready to forego or substitute for an additional unit of good 1. In other words, it represents the cost of good 1 that the consumer is ready to pay in terms of the other good. The MRS between two goods is given by the absolute value of the ratio of change in the consumption of good 2 to the change in the consumption of good 1. That is, \[MR{{S}_{1,2}}=\left| \frac{\Delta {{x}_{2}}}{\Delta {{x}_{1}}} \right|\] The IC is convex to the origin because of the diminishing MRS. As the consumer consumes more and more of one good, the marginal utility of the good falls. On the other hand, the marginal utility of the good which is sacrificed rises. In other words, the consumer is willing to sacrifice less and less for each additional unit of the other good consumed. Thus, as we move down the IC, MRS diminishes. This suggests the convex shape of indifference curve.
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