Lucinda is writing a coordinate proof to show that a diagonal of a parallelogram partitions the parallelogram into two equal areas. A parallelogram graphed on a coordinate plane. The vertices of rectangle are labeled as K L M and N. The vertex labeled as K lies on begin ordered pair 0 comma 0 end ordered pair. The vertex labeled as L lies on begin ordered pair x comma 2 y end ordered pair. The coordinate of vertex M is left blank. The vertex labeled as N lies on begin ordered pair 3 x comma 0 end ordered pair. A diagonal is drawn between points K and M.

Enter your answers in the boxes to complete Lucinda's proof.

Since KLMN is a parallelogram and a parallelogram's opposite sides are parallel and congruent, the coordinates for M are (4x, 2y).

In △KMN, the length of the base is and the height is . So an expression for the area of △KMN is .

In △KLM, the length of the base is 3x and the height is 2y. So an expression for the area of △KLM is .

Comparing the area of the two triangles that are formed by a diagonal of the parallelogram shows that a diagonal of a parallelogram partitions the parallelogram into two equal areas.

9514 1404 393

Step-by-step explanation:

The base length is the length of the horizontal line segment KN. That length is the difference of the x-coordinates: 3x -0 = 3x.

The height is the difference of the y-coordinate of point M and the y-coordinate of horizontal segment KN. That difference is 2y -0 = 2y.

The area is half the product of base and height:

  A = (1/2)bh

  A = 1/2(3x)(2y) = 3xy

In ΔKMN, the length of the base is 3x and the height is 2y. So an expression for the area of ΔKMN is 3xy.

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In ΔKLM, the length of the base is 3x and the height is 2y. So an expression for the area of ΔKLM is 3xy.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

answer: b)

step-by-step explanation:

its a dot plot because since the score is not high numbers.

- r3ktforgood ☕