Question

the distance between the lines 2x+4=0 and x-5=0 is
a) 9 units
b) 1 unit
c) 5 units
d) 7 units​

Answer 1

it is given that in first line

2x+4=0

solving the  equation  we get

x = -4/2

= -2

hence there is no  y coordinate.

hence, first point (-2,0)

now  for second line

x-5=0

solving the equation we get

x=5

hence there is no y coordinate

hence second point is  (5,0)

The distance between the two points = √[{5-(-2)}² + (0-0)²]

= √(5+2)²

= √7²

= 7 units

hence finally we can say that Option (D) is correct.

Answer 2

The distance between lines $2x+4=0$ and $x-5=0$ is d) 7 units.

Step-by-step explanation:

Given:

First equation: $2x+4=0$

Second equation: $x-5=0$

To find: Distance between the two equations.

Solution:

First equation:

$2x+4=0\\x=-4/2\\x=-2$

Second equation:

$x-5=0\\x=5$

Now, the lines for $x=-2$ and $x=5$ is graphically drawn (below picture) and the distance between both the lines is calculated. Also we can numerically calculate it as $5-(-2)=7$ units.

The distance between $-2$ and $5$ is $7$ units.