Question

Shahriyar is at a winter park with his family. They go sledding first, then ice skating, then skiing. What is the total distance traveled

between these locations?
(1 point)

Answer 1

Shahriyar's family covered 16 miles sledding from (2, 12) to (2, -4) and 10 miles skating from (2, -4) to (-8, -4). The total distance traveled is 26 miles.

Let's break down the total distance traveled by Shahriyar's family step by step:

Step 1: Distance from Sledding to Ice Skating

Given coordinates for sledding and ice skating are (2, 12) and (2, -4) respectively.

`\[d_{\text{sledding to skating}} = √((2 - 2)^2 + (-4 - 12)^2)\]\[d_{\text{sledding to skating}} = √(0 + 16^2)\]\[d_{\text{sledding to skating}} = √(256)\]\[d_{\text{sledding to skating}} = 16 \text{ miles}\]`

Step 2: Distance from Ice Skating to Skiing

Given coordinates for ice skating and skiing are (2, -4) and (-8, -4) respectively.

`\[d_{\text{skating to skiing}} = √((-8 - 2)^2 + (-4 + 4)^2)\]\[d_{\text{skating to skiing}} = √((-10)^2 + 0)\]\[d_{\text{skating to skiing}} = √(100)\]\[d_{\text{skating to skiing}} = 10 \text{ miles}\]`

Step 3: Total Distance Traveled

`\[d_{\text{total}} = d_{\text{sledding to skating}} + d_{\text{skating to skiing}}\]\[d_{\text{total}} = 16 \text{ miles} + 10 \text{ miles}\]\[d_{\text{total}} = 26 \text{ miles}\]`

Therefore, the total distance traveled by Shahriyar's family is 26 miles.

The complete question is:

Shahriyar is at a winter park with his family. They go sledding first, then ice skating, then skiing. What is the total distance traveled between these locations?