In the standard (x,y) coordinate plane, a parallelogram has vertices A(1, 2), B(6, 2), and… — ACT

In the standard $(x,y)$ coordinate plane, a parallelogram has vertices $A(1, 2)$ , $B(6, 2)$ , and $C(8, 6)$ . If the fourth vertex, $D$ , has a $y$ -coordinate of $6$ and lies to the left of $C$ , what is the $x$ -coordinate of $D$ ?

A
$-7$
$3$ Cevap
C
$5$
D
$9$
E
$13$

Cevap

The correct answer is

3

, which is the

x

-coordinate of vertex

D

The correct answer is the coordinate value

3

. Since vertices

A(1, 2)

and

B(6, 2)

share the same

y

-coordinate, the side

AB

is horizontal with a length of

6 - 1 = 5

units. The opposite side

CD

must also be horizontal and have the same length of

5

units. Since vertex

C

is at

(8, 6)

and vertex

D

lies to its left, the

x

-coordinate of

D

is found by subtracting

5

from the

x

-coordinate of

C

, which gives

8 - 5 = 3

Adım Adım Çözüm

Identify the relationship between the vertices of the parallelogram.

Sides

AB

and

CD

are parallel and equal in length.

By definition, opposite sides of a parallelogram are equal in length and parallel.

Calculate the horizontal length of the bottom side

AB

Length of

AB = 6 - 1 = 5

units.

Since both

A(1,2)

and

B(6,2)

share a

y

-coordinate of

2

, the segment is horizontal, and its length is the difference in their

x

-coordinates.

Apply the horizontal translation to find the

x

-coordinate of

D

x = 8 - 5 = 3

Since

D

lies to the left of

C(8,6)

on the horizontal line

y=6

, we subtract the side length of

5

units from the

x

-coordinate of

C

to get the

x

-coordinate of

D

Anahtar Kavram

Using the properties of parallelograms and coordinates on a 2D plane to find a missing vertex.

Tahmini Süre:45s

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Cevap

Adım Adım Çözüm

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