PLEASE HELP!!
Which of the following points could be added to the graph to create a square? Choose all that apply.
A coordinate grid is shown with two points plotted. Point A is located at left-parenthesis negative 2 comma 3 right-parenthesis. Point B is located at left-parenthesis 3 comma 3 right-parenthesis.
A. left-parenthesis negative 2 comma negative 2 right-parenthesis
B. left parenthesis negative 2 comma negative 3 right parenthesis
C. left parenthesis 3 comma negative 2 right parenthesis
D. left parenthesis 3 comma negative 3 right parenthesis
A. left-parenthesis negative 2 comma negative 2 right-parenthesis
C. left parenthesis 3 comma negative 2 right parenthesis
D. left parenthesis 3 comma negative 3 right parenthesis
PLEASE HELP!!!
Which of the following points could be added to the coordinate graph as a third point to create an isosceles triangle? Choose all that apply.
A coordinate grid is shown with two points plotted. Point A is located at left-parenthesis negative 2 comma 0 right-parenthesis. Point B is located at right-parenthesis 4 comma 0 right-parenthesis.
A. left parenthesis 1 comma 3 right parenthesis
B. left parenthesis negative 2 comma 5 right parenthesis
C. left parenthesis 1 comma negative 6 right parenthesis
D. left parenthesis 4 comma negative 2 right parenthesis
A. left parenthesis 1 comma 3 right parenthesis
D. left parenthesis 4 comma negative 2 right parenthesis
To create a square, we need to add two more points that are the same distance from points A and B and form right angles with the given points.
Let's check the distance between point A (x₁, y₁) with coordinates (-2, 3) and point B (x₂, y₂) with coordinates (3, 3):
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
= √((3 - (-2))² + (3 - 3)²)
= √((3 + 2)² + (0)²)
= √(5² + 0²)
= √(25 + 0)
= √25
= 5
Now, let's find coordinates that are 5 units away from point A and form right angles with points A and B.
Possible answers:
A. (-2, -2): The distance between (-2, 3) and (-2, -2) is √(((-2) - (-2))² + ((-2) - 3)²) = √(0² + (-5)²) = √(0 + 25) = √25 = 5. This point can be added to form a square.
B. (-2, -3): The distance between (-2, 3) and (-2, -3) is √(((-2) - (-2))² + ((-3) - 3)²) = √(0² + (-6)²) = √(0 + 36) = √36 = 6. This point cannot be added to form a square since it is not 5 units away from point A.
C. (3, -2): The distance between (-2, 3) and (3, -2) is √((3 - (-2))² + ((-2) - 3)²) = √(5² + (-5)²) = √(25 + 25) = √50. This point cannot be added to form a square since it is not 5 units away from point A.
D. (3, -3): The distance between (-2, 3) and (3, -3) is √((3 - (-2))² + ((-3) - 3)²) = √(5² + (-6)²) = √(25 + 36) = √61. This point cannot be added to form a square since it is not 5 units away from point A.
Based on the calculations, the point that can be added to form a square is A. (-2, -2).