Question

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.

Answer 1

Explanation:

Mr. Johnson is constructing a square table for his classroom. He positioned his design on a coordinate grid, shown in the attached picture. 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 this first find the slope of both diagonals:

AC= y2-y1/ x2-x1

AC= -5- 2/ 4-(-3)

AC= -7/7

AC = -1

BD = y2-y1/ x2-x1

BD= 2-(-5)/ 4-(-3)

BD = 7/7

BD= 1

Thus the product of both the slopes = -1*1 = -1

AC and BD are perpendicular

The slopes of perpendicular lines in a coordinate plane are opposite reciprocals of each other.

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