Question

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question 18
pooja shops at two different grocery stores. the locations of her home and the stores are shown in the table.

location

coordinates

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poojas home

$(-1.75, -2)$

acme market

$(-1.75, -0.5)$

natural foods

$(-2.25, -2)$

which grocery store is a shorter distance from poojas home?

Explanation:

Step1: Recall distance formula

The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.

Step2: Calculate distance to Acme Market

Pooja's home: $(-1.75,-2)$, Acme Market: $(-1.75,-0.5)$

$$\begin{align*} d_1&=\sqrt{(-1.75-(-1.75))^2+(-0.5-(-2))^2}\\ &=\sqrt{0^2+(1.5)^2}\\ &=1.5 \end{align*}$$

Step3: Calculate distance to Natural Foods

Pooja's home: $(-1.75,-2)$, Natural Foods: $(-2.25,-2)$

$$\begin{align*} d_2&=\sqrt{(-2.25-(-1.75))^2+(-2-(-2))^2}\\ &=\sqrt{(-0.5)^2+0^2}\\ &=0.5 \end{align*}$$

Step4: Compare the two distances

$0.5 < 1.5$, so Natural Foods is closer.

Answer:

Natural Foods