Question

What are the coordinates of point S"? (negative three-halves, nine-halves) (negative nine-halves, fifteen-halves) (nine-halves, negative three-halves) (negative fifteen-halves, 0)

Answer 1

Answer:

$S=(\frac{9}{2},-\frac{3}{2})$

Step-by-step explanation:

The missing details are:

$T= (0,4)$

$M = (\frac{9}{4}, \frac{5}{4})$ --- Midpoint of ST

Required

Determine the coordinates of S

To do this, we apply the mid-point formula:

$M(x,y) = \frac{1}{2}(x_1+x_2,y_1+y_2)$

Where

$M(x,y) = (\frac{9}{4}, \frac{5}{4})$

$T(x_1,y_1) - (0,4)$

The equation becomes:

$M(x,y) = \frac{1}{2}(x_1+x_2,y_1+y_2)$

$(\frac{9}{4},\frac{5}{4}) = \frac{1}{2}(0+x_2,4+y_2)$

$(\frac{9}{4},\frac{5}{4}) = \frac{1}{2}(x_2,4+y_2)$

Multiply through by 2

$2*(\frac{9}{4},\frac{5}{4}) = 2*\frac{1}{2}(x_2,4+y_2)$

$(\frac{9}{2},\frac{5}{2}) = (x_2,4+y_2)$

By comparison:

$x_2 = \frac{9}{2}$

$4 + y_2 =\frac{5}{2}$

$y_2 =\frac{5}{2}-4$

$y_2 =\frac{5-8}{2}$

$y_2 =-\frac{3}{2}$

Hence, the coordinates of S is:

$S=(\frac{9}{2},-\frac{3}{2})$