Mathematics: Tell whether the lines for each pair of equations are parallel, perpendicular, or neither. y=-2x+4 -5x+10y=5 a: parallel b: perpendicular c: neither tell whether the lines for each pair of equations are parallel, perpendicular, or neither. y=(-1/5)x+6 -2x+10y=5 a: parallel b: perpendicular c: neither

A rigid transformation is a geometric transformation. a dilation is not a rigid transformation because it does not preserve distance....

Tell whether the lines for each pair of equations

Ответ:

thegurl41

20.06.2020

Mathematics

The correct options are

(1) (B) parallel

(2) (C) neither.

Step-by-step explanation: We know that two straight lines are

(i) parallel, if they have equal slopes,

(ii) perpendicular, if the product of their slopes is -1.

Also, the slope-intercept form of the equation of a straight line is

y=mx+c, where m is the slope.

(1) We are given to check whether the following lines are parallel, perpendicular or neither :

$y=-2x+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\5x+10y=5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Comparing equation (i) with the slope-intercept form, we get

m_1=-2.

From equation (ii), we have

$-5x+10y=5\\\\\Rightarrow -x+2y=1\\\\\Rightarrow 2y=x+1\\\\\Rightarrow y=\dfrac{1}{2}x+\dfrac{1}{2}.$

So, $m_2=\dfrac{1}{2}.$

We have

$m_1\times m_2=(-2)\times\dfrac{1}{2}=-1.$

Therefore, the given lines are perpendicular.

Option (B) is CORRECT.

(2) We are given to check whether the following lines are parallel, perpendicular or neither :

$y=-\dfrac{1}{5}x+6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)\\\\-2x+10y=5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)$