Give the coordinates of \( B \) under a dilation about point \( T \) with scale factor \( \frac{3}{2} \). \( B(-8,-4) \) \( T(-4,-5) \)

To find the coordinates of point \( B' \) after dilation about point \( T \) with a scale factor of \( \frac{3}{2} \), we can use the formula: \[ B' = T + k(B - T) \] where \( k \) is the scale factor. First, we calculate \( B - T \): \[ B - T = (-8 - (-4), -4 - (-5)) = (-8 + 4, -4 + 5) = (-4, 1) \] Now we apply the scale factor \( \frac{3}{2} \): \[ k(B - T) = \left(\frac{3}{2}(-4), \frac{3}{2}(1)\right) = \left(-6, \frac{3}{2}\right) \] Now we add this result to point \( T \): \[ B' = T + k(B - T) = \left(-4, -5\right) + \left(-6, \frac{3}{2}\right) = (-4 - 6, -5 + \frac{3}{2}) = (-10, -\frac{10}{2} + \frac{3}{2}) = (-10, -\frac{7}{2}) \] Thus, the coordinates of \( B' \) after dilation are: \[ B'\left(-10, -\frac{7}{2}\right) \]