Question

Erik draws quadrilateral ABCD
. If side AB=40x
, side BC=4+3y
, side CD=8x+32
, and side AD=9y−20
, for what values of x and y can Erik be sure that his quadrilateral is a parallelogram?(1 point)
Responses

x=4
and y=1
x equals 4 and y equals 1

x=20
and y=8
x equals 20 and y equals 8

x=1
and y=4
x equals 1 and y equals 4

x=40
and y=16
Answer
When the three medians of the triangle are drawn, they meet at a single point. What is the point of the centroid?

medians are A= (5,5) B= (1,7) C= (3,2)

(1 point)
Responses

(3,5)

(103,133)

(3,6)

(3,143)
Answer
Given the rectangle ABCD
as shown, find the value for x if DO=4x+8
and CO=15x−3
.
Answer
Lines AC¯¯¯¯¯¯¯¯
and BD¯¯¯¯¯¯¯¯
are diagonals of ABCD
. What value of x makes ABCD
a rectangle if AC=x+7
and BD=3x−5
?

(1 point)
Responses

x=6
x equals 6

x=15
x equals 15

x=8
x equals 8

x=13
Answered by GPT 3.5
x equals 40 and y equals 16
Answered by GPT 3.5
The point of the centroid can be found by finding the average of the coordinates of the medians.

The coordinates of the centroid can be calculated as follows:

x-coordinate of centroid = (x-coordinate of A + x-coordinate of B + x-coordinate of C) / 3
= (5 + 1 + 3) / 3
= 9 / 3
= 3

y-coordinate of centroid = (y-coordinate of A + y-coordinate of B + y-coordinate of C) / 3
= (5 + 7 + 2) / 3
= 14 / 3
= 4.67

Therefore, the point of the centroid is (3, 4.67). But since we are given only integer coordinate options, the closest option is (3, 5). So the correct response is:

(3,5)
Answered by GPT 3.5
Since AD and BC are parallel sides of a rectangle, we know that they are equal in length. Therefore, DO = CO.

4x + 8 = 15x - 3

To solve for x, we can subtract 4x from both sides and add 3 to both sides:

8 + 3 = 15x - 4x

11 = 11x

Dividing both sides by 11, we get:

x = 1

Therefore, the value of x is 1.
Answered by GPT 3.5
In a rectangle, the diagonals are equal in length. Therefore, AC = BD.

x + 7 = 3x - 5

To solve for x, we can subtract x from both sides and add 5 to both sides:

7 + 5 = 3x - x

12 = 2x

Dividing both sides by 2, we get:

x = 6

Therefore, the value of x that makes ABCD a rectangle is x = 6.