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
x equals 40 and y equals 16
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)
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.
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)
Given the rectangle ABCD
as shown, find the value for x if DO=4x+8
and CO=15x−3
.
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
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.