Question

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

Quadrilateral FGHI is shown on the coordinate plane with coordinates F at negative 6, negative 1. G at negative 1, negative 1. H at negative 2, negative 4. I negative 7, negative 4. Point A is at 3, 8 and point D is at 1, 2.
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(3, 8) and point D(1, 2), what is another point that could represent a corner of the trail?

a) (10, 8)
b)(6, 8)
c) (8, 8)
D) (13, 8)

Answer 1

Answer: D) (13, 8)

:)))

Answer 2

The correct option is D.

Explanation:

From the given figure it is noticed that the vertices of the parallelogram are F(-6,-1), G(-1,-1), H(-2,-4) and I(-7,-4).

In order to build a scale model of the trail, the drawing is enlarged on the coordinate plane.

Distance formula

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

`FI=√((-7-(-6))^2+(-4-(-1))^2)=√(1+9)=√(10)`

`AD=√((1-3)^2+(2-8)^2)=√(4+36)=2√(10)`

The scale factor is

`(AD)/(FI)=(2√(10))/(√(10))=2`

Therefore the length of sides of image is twice of preimage.

The vertices A and D are image of F and I respectively.

The length of FG is

`FG=√((-1-(-6))^2+(-1-(-1))^2)=√(25)=5`

Therefore the length of AB is 10 units and length of CD is also 10 units.

The point which is on horizontal distance of 10 units from A(3,8), is B(13,8).

The point which is on horizontal distance of 10 units from D(1,2), is C(11,2).

Therefore vertices B and C are image of G and H respectively. The another corner points are (13,8) and (11,2). Option D is correct.