Question

If line 2x+y=-3 and x-2y=1 form the sides of a
rectangle whose other sides meet at the point
(3, 4), find the equations of the other sides and
the area of the rectangle

plz help show solution step

Answer 1

y = -2x -3 the slope = -2
y = (1/2)x - 1/2 slope = 1/2 so perpendicular, whew that helps.
where do they cross? That is a corner.

(x-1)/2 = -2x-3
x-1 = -4x -6
5x = -5
x=-1
y = 2-3 = -1
so other corner is (-1, -1)
now draw it and find the other two intersetions

Answer 2

One side is the distance from (3,4) to 2x+y+3=0

The other side is the distance from (3,4) to x-2y-1=0

The area of the rectangle is thus

|2*3+1*4+3)/√(2^2+1^2) * |1*3-2*4-1|/√(1^2+2^2) = 13

Answer 3

Where did the √2^2+1^2 come from
Try to break it down please it's confusing

Answer 4

How did you get the 13
It's giving me -78/6