Question

M&P is showing on the graph below if QRS has coordinates Q ( -6 ,- 7 ) and R(-8,-1) what could be the coordinates of S if MNP = QRS?

Answer 1

The calculated coordinates of S if MNP = QRS are (-10, -12)

What could be the coordinates of S if MNP = QRS?

From the question, we have the following parameters that can be used in our computation:

Triangle QRS

Also, we have

Q(-6 ,-7) and R(-8,-1)

From the graph, we have

M(1 ,3) , N(7, 5) and P(-3,-2)

The translation from MNP to QRS using points M and Q are

(x, y) = (x - 1 - 6, y - 3 - 7)

(x, y) = (x - 7, y - 10)

This means that

S = (-3 - 7, -2 - 10)

S = (-10, -12)

Hence, the coordinates of S are (-10, -12)

Answer 2

Lets draw a picture of our points:

since triangles are similar the following ratios must be preserved:

`\begin{gathered} \text{ratioX}=\frac{\text{xred}}{\text{xgreen}} \\ \text{ratioY=}\frac{\text{yred}}{ygreen} \end{gathered}`

where these values come from the following picture:

for the first x red-ratio, we have

`\text{ratioX}=(8-6)/(3-2)=(2)/(1)=2`

for green-ratio, we have

`\text{ratioY}=(7-1)/(3-(-2))=(6)/(5)`

Then, by applying these results, the ratios from point S=(x,y) to point N=(7,5) must be

`\begin{gathered} (x)/(7)=2 \\ (y)/(5)=(6)/(5) \end{gathered}`

From the first relation, we get

`x=7*2=14`

and from the second relation, we have

`y=5*(6)/(5)=6`

then, the searched point S has coordinates S=( 14,6)