Question
Find the distance between the points left-parenthesis 4 comma 3 right-parenthesis and left-parenthesis 2 comma negative 1 right-parenthesis. Express your answer in simplest radical form.
(1 point)
Responses
2 Start Root 10 End Root
Image with alt text: 2 Start Root 10 End Root
2 Start Root 5 End Root
Image with alt text: 2 Start Root 5 End Root
2 Start Root 3 End Root
Image with alt text: 2 Start Root 3 End Root
2 Start Root 2 End Root
Image with alt text: 2 Start Root 2 End Root
To find the distance between two points, we can use the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of the two points are (4, 3) and (2, -1).
Plugging these values into the distance formula, we get:
distance = sqrt((2 - 4)^2 + (-1 - 3)^2)
= sqrt((-2)^2 + (-4)^2)
= sqrt(4 + 16)
= sqrt(20)
Therefore, the distance between the two points is 2sqrt(5), which is the simplified radical form of sqrt(20).
So the correct answer is: 2 Start Root 5 End Root.