Answer:
The x-coordinate of point B that bisects AC is [tex]\frac{9}{2}[/tex].
Step-by-step explanation:
The statement is not correct, the correct form is:
Jane drew a point A located at (-3,0) and point Clocated at (12,-6). What is the x-coordinate of point B that bisects AC?
Where a point bisects a segment, it means that segment is divided into two equal parts. If we know that [tex]\vec A = (-3, 0)[/tex] and [tex]\vec C = (12, -6)[/tex] are endpoints of the segment, the location of the endpoint can be found by the following vectorial formula:
[tex]\vec B = \vec A + \frac{1}{2}\cdot \overrightarrow {AC}[/tex]
[tex]\vec B = \vec A + \frac{1}{2} \cdot (\vec C-\vec A)[/tex]
[tex]\vec B = \frac{1}{2}\cdot \vec A + \frac{1}{2}\cdot \vec C[/tex]
[tex]\vec B = \frac{1}{2}\cdot (-3,0)+\frac{1}{2}\cdot (12,-6)[/tex]
[tex]\vec B = \left(-\frac{3}{2}, 0 \right)+\left(6,-3\right)[/tex]
[tex]\vec B = \left(-\frac{3}{2}+6, 0-3\right)[/tex]
[tex]\vec B = \left(\frac{9}{2},-3\right)[/tex]
The x-coordinate of point B corresponds to the first component of the ordered pair found above, that is, [tex]x_{B} = \frac{9}{2}[/tex].
The x-coordinate of point B that bisects AC is [tex]\frac{9}{2}[/tex].
