Answered

Point [tex][tex]$A$[/tex][/tex] is at [tex][tex]$(-7,-9)$[/tex][/tex] and point [tex][tex]$M$[/tex][/tex] is at [tex][tex]$(-0.5,-3)$[/tex][/tex].

Point [tex][tex]$M$[/tex][/tex] is the midpoint of points [tex][tex]$A$[/tex][/tex] and [tex][tex]$B$[/tex][/tex].

What are the coordinates of point [tex][tex]$B$[/tex][/tex]?



Answer :

GinnyAnswer
To determine the coordinates of point [tex]\( B \)[/tex], let's use the fact that point [tex]\( M \)[/tex] is the midpoint of the line segment connecting points [tex]\( A \)[/tex] and [tex]\( B \)[/tex]. The midpoint [tex]\( M(x, y) \)[/tex] of a segment with endpoints [tex]\( A(x_1, y_1) \)[/tex] and [tex]\( B(x_2, y_2) \)[/tex] can be found using the midpoint formula:

[tex]\[ M_x = \frac{A_x + B_x}{2}, \quad M_y = \frac{A_y + B_y}{2} \][/tex]

Given the coordinates of point [tex]\( A \)[/tex] as [tex]\( (-7, -9) \)[/tex] and the coordinates of the midpoint [tex]\( M \)[/tex] as [tex]\( (-0.5, -3) \)[/tex], we can set up the following system of equations:

[tex]\[ -0.5 = \frac{-7 + B_x}{2} \][/tex]
and
[tex]\[ -3 = \frac{-9 + B_y}{2} \][/tex]

First, solve for [tex]\( B_x \)[/tex]:

[tex]\[ -0.5 = \frac{-7 + B_x}{2} \][/tex]

Multiply both sides of the equation by 2 to eliminate the fraction:

[tex]\[ -1 = -7 + B_x \][/tex]

Add 7 to both sides of the equation to solve for [tex]\( B_x \)[/tex]:

[tex]\[ -1 + 7 = B_x \][/tex]

[tex]\[ B_x = 6 \][/tex]

Next, solve for [tex]\( B_y \)[/tex]:

[tex]\[ -3 = \frac{-9 + B_y}{2} \][/tex]

Multiply both sides of the equation by 2 to eliminate the fraction:

[tex]\[ -6 = -9 + B_y \][/tex]

Add 9 to both sides of the equation to solve for [tex]\( B_y \)[/tex]:

[tex]\[ -6 + 9 = B_y \][/tex]

[tex]\[ B_y = 3 \][/tex]

Thus, the coordinates of point [tex]\( B \)[/tex] are [tex]\( (6, 3) \)[/tex].

Other Questions