The coordinates of the point JJ are left parenthesis, minus, 4, comma, minus, 9, right parenthesis(−4,−9) and the coordinates of point KK are left parenthesis, minus, 4, comma, 3, right parenthesis, .(−4,3). What is the distance, in units, between the point JJ and point K, question markK?

1 answer

To find the distance between the points \( J(-4, -9) \) and \( K(-4, 3) \), we can use the distance formula, which is defined as:

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

Here, \( (x_1, y_1) \) represents the coordinates of point \( J \) and \( (x_2, y_2) \) represents the coordinates of point \( K \).

Substituting the coordinates into the formula:

\[ (x_1, y_1) = (-4, -9) \quad \text{and} \quad (x_2, y_2) = (-4, 3) \]

Now calculating the differences:

\[ x_2 - x_1 = -4 - (-4) = 0 \] \[ y_2 - y_1 = 3 - (-9) = 3 + 9 = 12 \]

Substituting these differences back into the distance formula:

\[ d = \sqrt{(0)^2 + (12)^2} = \sqrt{0 + 144} = \sqrt{144} = 12 \]

Thus, the distance between points \( J \) and \( K \) is \( 12 \) units.