Question

Parallelogram FGHI on the coordinate plane below represents the drawing of a horse trail through a local park.



In order to build a scale model of the trail, the drawing is enlarged on the coordinate plane. If two corners of the trail are at point A (0, 4) and point D (-6, -5), what is another point that could represent a corner of the trail?

(9, -5)

(6, -5)

(12, -5)

(3, -5)

Answer 1

@SmoothMath

Answer 2

I think its the first one but im not sure... just need someone to check my answer for me(:

Answer 3

You have to count the slope from F to I and from D to A to see what the scale factor is

Answer 4

Or you can use the distance formula

Answer 5

@J.L. for F to I i got 2 over 3 and for A to D i got 6 over 9

Answer 6

So the scale factor is 3, now apply it to the distance of one of the sides of the smaller parallelogram

Answer 7

@Math_Is_Confusing123 first. Find the distance of IF and then DA.
\[d = \sqrt{(x_{1} - x_2)^2 + (y_1 - y_2)^2}\]Can you find the two distances?

Answer 8

@Calcmathlete isn't the distance formula the other way around?\[\sqrt{(x _{2}-x _{1})^{2}+(y _{2}-y _{1})^{2}}\]

Answer 9

Either or works. Since it's squared in the end, it doesn't metter. It's pretty much the absolute value of the distances.

Answer 10

for IF the distance is \[\sqrt{13}\] and the distance for DA is \[\sqrt{117}\]

@Calcmathlete

Answer 11

Alright. Now, let's simplify the radical. \[\sqrt{117} \implies 3\sqrt{13}\]Now that it's the same square root, let's set up a scale factor.
\[\frac{3\sqrt{13}}{\sqrt{13}} \implies 3\]See? the scale factor is one. Now count the distance of IH

Answer 12

*I mean the scale factor is 3.

Answer 13

the distance between I and H is 4. so i multiply that by 3 to get 12? and the answer is c?

Answer 14

When you count the distance of IH, it is 4. Set up a proportion.
\[\frac 31 = \frac x4\]\[x = 3(4)\]\[x = 12\]THis is the length of the bottom side of the enlarged parallelogram. Count 12 to the right of (-6, -5).

Answer 15

It is not C, but you're close :)
\[(-6 + 12, -5) \implies (? , -5)\]

Answer 16

Oh! okay i get it now!its 6,-5 B!

Answer 17

Yup :)

Answer 18

Yay! i get it now thanks so much(:

Answer 19

np :)