Question

complete the right isosceles triangle above. what could be the coordinates of the missing vertex?
a. (1, 9)
b. (1, 3)
c. (4, 3)
d. (1, 8)

Explanation:

Step1: Recall properties of right - isosceles triangle

In a right - isosceles triangle, two sides are of equal length and one angle is 90 degrees. The given line segment is horizontal from (1, 5) to (4, 5).

Step2: Determine possible right - angle vertex

For a right - isosceles triangle with the given horizontal segment, the missing vertex must be either directly above or below one of the endpoints of the given segment such that the two legs of the right - triangle are equal. If we consider the point (1, 5) as one of the endpoints, moving 2 units down (since the length of the given horizontal segment is \(4 - 1=3\) units) gives the point (1, 3). This will form a right - isosceles triangle with the right - angle at (1, 3).

Answer:

B. (1, 3)