Question

find midpoint of side BC of triangle ABC with A(1,-4) and midpoint of the side through A (2,-1)and (0,1)

Answer 1

The coordinates of M are (1,4).

Step-by-step explanation:

Let M be the mid-point of side BC.

A is at (1,-4)

Let P (2,-1) be the mid -point of AB and Q (0,1) is the mid-point of  side AC.

Let coordinates of B are ($x_1,y_1$) and coordinates of C are ($x',y')$

Mid-point formula:$x=\frac{x_1+x_2}{2},y=\frac{y_1+y_2}{2}$

P is the mid-point of side AB

By using the formula

$2=\frac{1+x_1}{2}$

$1+x_1=2\times 2=4$

$x_1=4-1=3$

$-1=\frac{-4+y_1}{2}$

$-1(2)=-4+y_1$

$-2+4=y_1$

$y_1=2$

The coordinates of B are (3,2).

Q is the mid-point of side AC

By using the formula

$0=\frac{x'+1}{2}$

$x'+1=0$

$x'=-1$

$1=\frac{y'-4}{2}$

$y'-4=2$

$y'=2+4=6$

The coordinates of C are (-1,6).

By using the formula

The coordinates of M are

$x=\frac{3-1}{2},y=\frac{2+6}{2}$

$x=\frac{2}{2}=1,y=\frac{8}{2}=4$

The coordinates of M are (1,4).

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Answer 2

solution and diagram

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