Mr. Johnson is working on constructing a square table for his classroom. He positioned his design on a coordinate grid, as shown. Mr. Johnson will need to put a brace through each diagonal of the table in order to secure the table's stability. On the directions that came with the brace, Mr. Johnson read, "if using more than one brace, the braces must intersect at exactly a right angle". Use the diagram above to label two diagonals (to represent each brace). Prove that the braces will intersect at a right angle and that the table will be stable. Complete your work in the space provided or upload a file that can display math symbols if your work requires it.

Given Mr. Johnson is working on constructing a square table for his classroom. He positioned his design on a coordinate grid, as shown. Mr. Johnson will need to put a brace through each diagonal of the table in order to secure the table's stability.

Now, if Johnson use more than one brace then we have to prove that the braces will intersect at a right angle.

From the figure we have to prove the diagonals AC and BD are at right angle. To prove above we have to find the slopes of both diagonals.

[tex]\text{Slope of AC=}\frac{y_2-y_1}{x_2-x_1}=\frac{-5-2}{4-(-3)}=\frac{-7}{7}=-1[/tex]

[tex]\text{Slope of BD=}\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-5)}{4-(-3)}=\frac{7}{7}=1[/tex]

[tex]\text{Product of their slopes=}-1\times 1=-1[/tex]

As we know, In a coordinate plane, the slopes of perpendicular lines are opposite reciprocals of each other i.e their product is equals to -1.

⇒ AC and BD are perpendicular

⇒ Braces which put through each diagonal intersect at right angle and the table will stable.