*PLEASE HELP* The equations of lines K, P,and M are given below
K: x+2y=6
P: 6x + 3y=12
M: -x+ 2y=10

which statement is true

*ANSWERS ARE IN THE PICTURE*

Step-by-step explanation:

Given the equations of the following line

K: x+2y=6

P: 6x + 3y=12

M: -x+ 2y=10

First we need to get the slpe of each line as shown;

For K:

K: x+2y=6

Rewrite in standard form;

2y = -x + 6

y = -1/2 x + 6/2

y = -1/2 + 3

Slope of K is -1/2

For P:

P: 6x + 3y=12

Rewrite;

3y = -6x + 12

y = -6/3 x + 12/3

y = -2x + 4

Slope of P is 2

For M;

M: -x+ 2y=10

Rewrite

2y = x + 10

y = 1/2 x + 10/2

y = 1/2 x + 5

Slope of M is 1/2

Taking the product of slope K and P

Mk * Mp = -1/2 * 2

Mk * Mp = -1

Since the slope of K and P is -1, hence line M and line P are perpendicular

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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