Question

Select the midpoint of side BC of triangle ABC with A[1,-4] and the midpoint of sides through A being [3,-1] and [0,-1]

Answer 1

Answer:

int: In the above question we have a triangle ABC in which D, E, and F are midpoints. Side AB has a mid-point D, Side AC has a midpoint E, and Side BC has a midpoint F. Co-ordinate of A, D, and E is given. We will use the midpoint formula to solve this question.

Complete step-by-step answer:

Drawing figure from the given data:

   

From the figure, we know that;

D is the midpoint of AB.

E is the midpoint of AC.

F is the midpoint of BC.

In triangle ABC,

Coordinates of A (1, -4)

Coordinates of D (2, -1)

Coordinates of E (0, -12)

We need to find the Coordinates of F which is a midpoint of BC.

Let the Coordinates of B be (x2,y2), C be (x3,y3), and F be (x,y).

Now, using midpoint formula, we will try to find the coordinates of B

Coordinates of B =1+x22=2 and −4+y22=−1

After solving above equation, we get;

Coordinates of B (3, 2)

Now, using midpoint formula, we will try to find the coordinates of C

Coordinates of C =1+x32=0 and −4+y32=−12

After solving above equation, we get;

Coordinates of C (-1, -20)

Now, using midpoint formula, we will try to find the coordinates of F

Coordinates of F =x2+x32=x and y2+y32=y

Putting the values in the above equations, we get;

=3−12=x and 2−202=y

After solving above equation, we get;

Coordinates of F (1, -5)

Note: In this type of problems usually students make mistakes by considering the end point coordinates as equals to the sum of another endpoint and midpoint coordinates. The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.

Step-by-step explanation: