A(-1,1) B(1,5), C(3,1) are the vertices of triangle ABC. if M is the midpoint of BC, find BM
length of BC
= √( (5-1)^2 + (1-3)^2)
= √(16+4) = √20
= 2√5
since BM = (1/2)BC
BM = √5
To find the midpoint of a line segment, you need to average the x-coordinates and the y-coordinates of the two endpoints.
Let's find the coordinates of point M, the midpoint of BC. The endpoints of BC are B(1,5) and C(3,1).
To find the x-coordinate of M, we average the x-coordinates of B and C:
x-coordinate of M = (x-coordinate of B + x-coordinate of C) / 2
= (1 + 3) / 2
= 4 / 2
= 2
To find the y-coordinate of M, we average the y-coordinates of B and C:
y-coordinate of M = (y-coordinate of B + y-coordinate of C) / 2
= (5 + 1) / 2
= 6 / 2
= 3
Therefore, the midpoint M has coordinates (2, 3).
Now, let's find the length of BM. To find the length of a line segment, you can use the distance formula.
The distance formula is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's use the coordinates of B(1, 5) and M(2, 3) to find the length of BM:
distance = √((2 - 1)^2 + (3 - 5)^2)
= √(1^2 + (-2)^2)
= √(1 + 4)
= √5
Therefore, the length of BM is √5 (approximately equal to 2.236).