What is the length of segment XY?On a coordinate plane, line X Y has points (negative 4, 0) and (3, 2).4.5 unitsStartRoot 45 EndRoot units startRoot 53 EndRoot units9 units
Mathematics · College · Thu Feb 04 2021
Answered on
To find the length of segment XY on a coordinate plane where point X has coordinates (-4, 0) and point Y has coordinates (3, 2), you can use the distance formula. The distance formula is derived from the Pythagorean theorem and is stated as:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the two points.
Here, \( x_1 = -4 \), \( y_1 = 0 \), \( x_2 = 3 \), and \( y_2 = 2 \).
Let's plug these into the formula:
\[ d = \sqrt{(3 - (-4))^2 + (2 - 0)^2} \] \[ d = \sqrt{(3 + 4)^2 + (2)^2} \] \[ d = \sqrt{7^2 + 2^2} \] \[ d = \sqrt{49 + 4} \] \[ d = \sqrt{53} \]
Therefore, the length of segment XY on the coordinate plane is \( \sqrt{53} \) units.