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H is the midpoint of
IG.

J is the midpoint of
IK.

IG=GK=10
Quantity A

IJ
Quantity B
5
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.

$H$ is the midpoint of $I G$ . $\newline$ $J$ is the midpoint of $I K$ . $\newline$ $I G=G K=10$ $\newline$ Quantity A $\newline$ $I J$ $\newline$ Quantity B $\newline$ $5$ $\newline$ Quantity A is greater. $\newline$ Quantity B is greater. $\newline$ The two quantities are equal. $\newline$ The relationship cannot be determined from the information given.

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Find instantaneous rates of change

Full solution

Q.

H

is the midpoint of

I G

.

\newline

J

is the midpoint of

I K

.

\newline

I G=G K=10

\newline

Quantity A

\newline

I J

\newline

Quantity B

\newline

5

\newline

Quantity A is greater.

\newline

Quantity B is greater.

\newline

The two quantities are equal.

\newline

The relationship cannot be determined from the information given.

Midpoint Calculation: $H$ is the midpoint of $IG$ , so $IH = HG = \frac{IG}{2}$ . $\newline$ Calculation: $IH = HG = \frac{10}{2} = 5$ .
Midpoint Calculation: $J$ is the midpoint of $IK$ , so $IJ = JK = \frac{IK}{2}$ . $\newline$ Calculation: $IJ = JK = \frac{10}{2} = 5$ .
Comparison with Quantity B: Now we compare $IJ$ with Quantity B, which is $5$ . $\newline$ Calculation: $IJ = 5$ , Quantity B = $5$ .
Conclusion: Since $IJ$ equals Quantity $B$ , we can conclude that the two quantities are equal.

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