Answer:
(6, 3) and (6, -4) or (-4, 3) and (-4, -4)
Explanation:
You want the coordinates of the remaining two vertices of a rectangle with area 35 square units, the endpoints of one side being (1, 3) and (1, -4).
Rectangle
A rectangle is a quadrilateral with adjacent sides at right angles. The area of it is the product of its length and width.
Dimensions
The given side is a vertical line (x=1) with points on it that are 7 units apart:
3 -(-4) = 7
The area being 35 square units means the length of an adjacent side must be ...
LW = 35
7W = 35
W = 35/7 = 5 . . . . units
The opposite side of the rectangle will be 5 units away, on a vertical line that is either x = 1+5 = 6, or x = 1 -5 = -4.
Coordinates
The y-coordinates of the endpoints of the opposite side will be the same as the y-coordinates of the given points. That is because the top and bottom edges of the rectangle are horizontal lines.
For the rectangle to the right of the given line, the missing coordinates are (6, 3) and (6, -4).
For the rectangle to the left of the given line, the missing coordinates are (-4, 3) and (-4, -4).
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Additional comment
The attachment shows the two possible sets of answers.