Question

The coordinates of the point XX are left parenthesis, minus, 2, comma, minus, 1, right parenthesis(−2,−1) and the coordinates of point YY are left parenthesis, minus, 10, comma, minus, 1, right parenthesis, .(−10,−1). What is the distance, in units, between the point XX and point Y, question markY?

Answer 1

To find the distance between the points \( X(-2, -1) \) and \( Y(-10, -1) \), we can use the distance formula for two points \( (x_1, y_1) \) and \( (x_2, y_2) \):

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Substituting the coordinates of points \( X \) and \( Y \):

• \( x_1 = -2 \), \( y_1 = -1 \)
• \( x_2 = -10 \), \( y_2 = -1 \)

Now plug these values into the distance formula:

\[ d = \sqrt{((-10) - (-2))^2 + ((-1) - (-1))^2} \] \[ d = \sqrt{(-10 + 2)^2 + (0)^2} \] \[ d = \sqrt{(-8)^2 + 0^2} \] \[ d = \sqrt{64 + 0} \] \[ d = \sqrt{64} \] \[ d = 8 \]

Thus, the distance between point \( X \) and point \( Y \) is \( \boxed{8} \) units.