Question

pre-algebra ic sem 2 fall 2025
finding distance in the coordinate plane
which points can be used in the diagram as the third vertex to create a right triangle with hypotenuse xy? choose two correct answers.
(2,4) (-2,1)
(3,4) (-2,-2)
(-4,-2)

Explanation:

Step1: Determine the coordinates of points X and Y

From the graph, assume \(X(-2,4)\) and \(Y(3, - 2)\)

Step2: Use the property of a right - triangle (the third vertex should form a vertical or horizontal line with either X or Y)

• For a point to form a right - triangle with \(XY\) as the hypotenuse, if we consider a horizontal line from \(X\) (where \(y = 4\)):
• The \(y\) - coordinate of \(X\) is \(y = 4\). If a point has \(y=4\) and a different \(x\) - coordinate from \(X\), and forms a right - angle with \(XY\). The point \((3,4)\) has \(y = 4\). The line segment from \(X(-2,4)\) to \((3,4)\) is horizontal (\(y\) - value is constant). Then we can check the right - angle condition.
• For a point to form a right - triangle with \(XY\) as the hypotenuse, if we consider a vertical line from \(X\) (where \(x=-2\)):
• The \(x\) - coordinate of \(X\) is \(x = - 2\). The point \((-2,-2)\) has \(x=-2\). The line segment from \(X(-2,4)\) to \((-2,-2)\) is vertical (\(x\) - value is constant)

Answer:

\((3,4)\), \((-2,-2)\)