How do you find the missing coordinate if P=(4,-1) is the midpoint of the segment AB, where A=(2, 5)?

Question

Abigail Allen · Accepted Answer

undefined To find the missing coordinate of point B, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (M) of a line segment with endpoints A(x₁, y₁) and B(x₂, y₂) can be found by taking the average of the x-coordinates and the average of the y-coordinates.

In this case, we are given that the midpoint (P) is (4, -1) and one endpoint (A) is (2, 5).

To find the missing coordinate of point B, we can use the midpoint formula:

x-coordinate of B = 2 * x-coordinate of P - x-coordinate of A
y-coordinate of B = 2 * y-coordinate of P - y-coordinate of A

Plugging in the given values, we have:

x-coordinate of B = 2 * 4 - 2 = 6
y-coordinate of B = 2 * (-1) - 5 = -7

Therefore, the missing coordinate of point B is (6, -7).

Avery Alexander · Answer

#B=(6,-7)#

Recall that the midpoint formula is:

#color(blue)(|bar(ul(color(white)(a/a)M=((x_1+x_2)/2,(y_1+y_2)/2)color(white)(a/a)|)))#

In your case:

Let #M=(4,-1)# Let #(x_1,y_1)=(2,5)# Let #(x_2,y_2)=#coordinate of B

Start by plugging your known values into the formula.

#(4,-1)=((2+x_2)/2,(5+y_2)/2)#

Since you are looking for #(x_2,y_2)#, the coordinates of B, you can treat the components of #x# and #y# to be two separate equations. For instance,

#4=(2+x_2)/2color(white)(XXXXXXXX)-1=(5+y_2)/2#

In each equation, solve for the variable.

#8=2+x_2color(white)(XXXXXXXxx)-2=5+y_2#

#x_2=6color(white)(XXXXXXXXXXXx)y_2=-7#

Hence, the coordinate of #B# is:

#B=color(green)(|bar(ul(color(white)(a/a)color(black)(((6,-7)))color(white)(a/a)|)))#