Question

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

Explanation:

Step1: Analyze the properties of a right - isosceles triangle

In a right - isosceles triangle, the two legs are of equal length and perpendicular to each other.

Step2: Determine the length of the given side

The given side is horizontal from \(x = 1\) to \(x = 4\) (since \(y=5\) is constant). The length of this side is \(4 - 1=3\) units.

Step3: Find the missing vertex

For a right - isosceles triangle, if we consider the right - angle, the missing vertex should be either \(3\) units below (since the given side is horizontal) or \(3\) units above. If we go \(3\) units below \(y = 5\) (keeping \(x = 1\)), we get \(y=5 - 2=3\) (because the side length is \(3\)). So the coordinates of the missing vertex are \((1,3)\)

Answer:

D. \((1,3)\)