IDNLearn.com is designed to help you find accurate answers with ease. Ask your questions and receive detailed and reliable answers from our experienced and knowledgeable community members.
Sagot :
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].
[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].
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.