Question

The diagram shows a path from Doint P to ponts consisting of three in somep(20.77oR1-4.-9)Q120,-9)S(-4,-24)What is the total length of the path from P to S?47 unitsb.55 units65 unitsd.73 units

Answer 1

b. 55 units

Step-by-step explanation

due to the displacements are vertical or horizontal we can add the length of each segmento to find the total,so

so

a)let

`\begin{gathered} P(20,7) \\ Q(20,-9) \end{gathered}`

`Distance\text{ from P to Q}\Rightarrow red`

as this is a vertical line, we nned to subtract the y-coomponet of the points

`\begin{gathered} Distance\text{ from P to Q=}\Delta y=7-(-9)=7+9=16 \\ so \\ PQ=16 \end{gathered}`

so , PQ= 16

Step 2

b) Distance from Q to R (green)

QR

Let

`\begin{gathered} Q(20,-9) \\ R(-4,-9) \end{gathered}`

as this is a horizontal line, we need to subtract the x-coomponet of the points ,so

`\begin{gathered} Distance\text{ fromQ to R=}\Delta x=20-(-4)=20+4 \\ so \\ QR=24 \end{gathered}`

so

QR=24

Step 3

finally, segment RS (blue)

let

`\begin{gathered} R(-4,-9) \\ S(-4,-24) \end{gathered}`

as this is a vertical line, we nned to subtract the y-coomponet of the points

`\begin{gathered} Distance\text{ fromR to S=}\Delta y=-9-(-24)=-9+24=15 \\ so \\ RS=15 \end{gathered}`

Step 4

finally , add the segments to find the total distance from P to S

`\begin{gathered} PS=PQ+QR+RS \\ replace \\ PS=16+24+15 \\ PS=55\text{ units} \end{gathered}`

therefore, the answer i

b. 55 units

I hope this helps you