Question

If (4,-3) is the midpoint of the line segment ST and the coordinates of S are (1,5), find the

Answer 1

Answer:

$(7,-11)$

Step-by-step explanation:

Given

$S = (1,5)$

$M = (4,-3)$

Required

Determine the coordinates of T

Midpoint is calculated as:

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

Where:

$(x,y) = (4,-3)$

$(x_1,y_1) = (1,5)$

Substitute these values in the above formula:

$(4,-3) = \frac{1}{2}(1 + x_2,5+y_2)$

Multiply through by 2

$2 * (4,-3) = 2 * \frac{1}{2}(1 + x_2,5+y_2)$

$(8,-6) = (1 + x_2,5+y_2)$

By direct comparison:

$1 + x_2 = 8$ and $5 + y_2 = -6$

Solving for x2

$1 + x_2 = 8$

$x_2 = 8 - 1$

$x_2 = 7$

Solving for y2

$5 + y_2 = -6$

$y_2 = -6 - 5$

$y_2 = -11$

Hence, the coordinates of T is: $(7,-11)$