Question

a square has an area of 36 and one side that lies along the line y=3. what could be the location of one of the vertices of this shape? a) (9, 4) b) (-5, -3) c) (6, 5) d) (3, 6)

Answer 1

Correct answer is:

b) (-5, -3)

Explanation:

Given that area of square is 36 and one sides lies along the line y = 3

To find:

Possible location of a vertex can be = ? Answer to be chosen from the options:

a) (9, 4)

b) (-5, -3)

c) (6, 5)

d) (3, 6)

Solution:

First of all, let us try to find the side of square.

`Area = Side^2 \\\Rightarrow Side^2 = 36\\\Rightarrow Side = 6`

Now, given that one side lies on the line y = 3 that means 2 of its coordinates will have their y - coordinates as 3.

Now, we know that all the angles of a square are
`90^\circ`.

So, coordinates of adjacent vertices will have a change in only x value or either y value.

Therefore, we can say that The other two coordinates of the square will have the y coordinates the value either 3 + 6 = 9 or 3 -6 = -3

One such possible square is attached in the answer area.

`\therefore` possible location of the one of the vertex is:

b) (-5, -3)