Question

23.) Using the map shown, the highway department locates two exits between Tomstownand Mount Lookout. From Tomstown, Exit 1 is halfway to Mount Lookout, and Exit 2is three-fourths of the way to Mount Lookout.Mount Lookout (78, 71)Bit 2Tomstown (2, 3)What are the coordinates for Exit 2?A (74, 37)B (59, 54)C (40, 37)D (68, 54)

Answer 1

In the figure, the coordinates of exit 2 is (59 54)

b. (59 54)

How to find the coordinates of exit 2

The coordinate of exit 2 is solved is three -fourths of the total length

Examining the figure, Tomstown (2, 3) takes 1 part while Mount Lookout (78, 71) takes 3 parts

Using ratio 3:1 we share as follows

X = (78 * 3 + 2 * 1) / (1 + 3)

X = (235 + 2) / (4)

X = 236/4

X = 59

Y = (71 * 3 + 1 * 1) / (1 + 3)

Y = (213 + 3) / (4)

Y = (216) / 4

Y = 54

The coordinates of exit 2 is (59 54)

Answer 2

Let's begin by listing out the information given to us:

`\begin{gathered} Towstown(T)\colon(2,3) \\ MountLookut(M)\colon(78,71) \end{gathered}`

Exit 1 is halfway to Mount Lookout & Exit 2 is 3/4 of the way to Mount Lookout. We have it thus:

`\begin{gathered} |MT|=(78-2,71-3)=(76,68) \\ |MT|=(76,68) \\ At\text{ Exit 2, we have the distance to be:} \\ (3)/(4)|MT|\Rightarrow(3)/(4)(76,68) \\ \Rightarrow(57,51) \\ Exit\mleft(2\mright)=(57,51)+(2,3) \\ Exit(2)=(57+2,51+3)=(59,54) \\ Exit(2)=(59,54) \end{gathered}`