What is the distance between the points (-3,12) and (-10,-8) 7 A. sqrt (185) B. sqrt (229) C. sqrt (351) D. sqrt (449)

To find the distance between two points \((-3, 12)\) and \((-10, -8)\), we use the distance formula:<br /><br />\[<br />d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}<br />\]<br /><br />Here, \((x_1, y_1) = (-3, 12)\) and \((x_2, y_2) = (-10, -8)\).<br /><br />First, calculate the differences in the coordinates:<br /><br />\[<br />x_2 - x_1 = -10 - (-3) = -10 + 3 = -7<br />\]<br /><br />\[<br />y_2 - y_1 = -8 - 12 = -20<br />\]<br /><br />Next, square these differences:<br /><br />\[<br />(-7)^2 = 49<br />\]<br /><br />\[<br />(-20)^2 = 400<br />\]<br /><br />Now, add these squared differences:<br /><br />\[<br />49 + 400 = 449<br />\]<br /><br />Finally, take the square root of the sum:<br /><br />\[<br />d = \sqrt}<br />\]<br /><br />Thus, the distance between the points \((-3, 12)\) and \((-10, -8)\) is:<br /><br />\[<br />\boxed{\sqrt{449}}<br />\]<br /><br />So the correct answer is:<br /><br />D. \(\sqrt{449}\)