Hi Anusha,

Kindly retype answer choices, above is not clear.

There are two ways solving this,

1. Use the formula

2. Plotting the points

Note: These are two lines are parallel,

x+y = 3 –> y = -x+3 –> So, slope is -1

2x+2y = 8 –> y = -x+ 4 –> So, slope again is -1. So they are parallel

After this just find the x and y intercepts of the lines and plot it.

x+y=3

(3,0) and (0,3)

x+y = 4

(4,0) and (0,4)

If we plot these you will find two isosceles triangles,

Drop a perpendicular as shown above, to find the shortest distance,

In the diagram shown above, the triangle MXN is isosceles right triangle,

So sides should be in the ratio of 1:1: sqrt(2)(angles: 45-45-90)

So, here distance has to be length opposite to the side 45 degrees .

so the shortest distance has to be,  1/sqrt(2) or we can write it as sqrt (2)/2

OR

Use the formula, shortest distance between two parallel lines = |b-c|/(sqrt(m^2 +1))

b and c intercepts and m is the slope.

you just need to substitute the values and get an answer.

Hope this helps.