Question

Use the graph of $\triangle ABC$ to find the coordinates of the endpoints of midsegment $\overline{EF}$ , which is opposite $\overline{AB}$ .

Answer 1

To find the endpoints of midsegment EF in triangle ABC with AB = BC, calculate the midpoints of sides AC and BC, which will be the endpoints of EF.

Step-by-step explanation:

To find the coordinates of the endpoints of midsegment ï¼EF, opposite ï¼AB in ⓦABC, we first need to identify the midpoints of the sides of the triangle that are not part of ï¼AB. If AB = BC = r, we can assume that triangle ABC is isosceles with AB and BC as its equal sides. Then the midpoint of ï¼AC and ï¼BC will form the endpoints of the midsegment EF.

Let the coordinates of A, B, and C be A(x1, y1), B(x2, y2), and C(x3, y3) respectively. The midpoint M of AC is found by averaging the x and y coordinates of A and C: M((x1+x3)/2, (y1+y3)/2). The same procedure is used to find the midpoint N of BC: N((x2+x3)/2, (y2+y3)/2). The segment EF is the line segment that connects M and N, and its endpoints are the coordinates of M and N.