1.) An isosceles triangle ΔABC has its altitude at the y-axis and its base at the x-axis. D is the midpoint of segment AC and E is the midpoint of segment CB. Given the coordinates A(-2a, 0), B(2a, 0), and C(0, 2b), determine the coordinates of midpoints D and E.
a.)D(2a,-b); E(-a,b)
b.)D(-a,b); E(a,b)
c.)D(0,2b); E(2a,0)
Draw a sketch with an x and y axis, that would show
you that b is the correct answer.
Thanks:)
To determine the coordinates of the midpoints D and E of the isosceles triangle ΔABC, we need to find the average of the coordinates of each pair of corresponding vertices.
Let's start by finding the coordinates of midpoint D. The coordinates of point A are (-2a, 0), and the coordinates of point C are (0, 2b). To find the midpoint D, we take the average of the x-coordinates and the y-coordinates separately.
Average of x-coordinates: (-2a + 0) / 2 = -a
Average of y-coordinates: (0 + 2b) / 2 = b
Therefore, the coordinates of midpoint D are (-a, b).
Next, let's find the coordinates of midpoint E. The coordinates of point C are (0, 2b), and the coordinates of point B are (2a, 0). Similar to finding midpoint D, we find the average of the x-coordinates and the y-coordinates.
Average of x-coordinates: (0 + 2a) / 2 = a
Average of y-coordinates: (2b + 0) / 2 = b
Therefore, the coordinates of midpoint E are (a, b).
Comparing the calculated coordinates with the given options:
a.) D(2a, -b); E(-a, b)
b.) D(-a, b); E(a, b)
c.) D(0, 2b); E(2a, 0)
We can see that the correct answer is option b.), which matches the calculated coordinates for midpoint D (-a, b) and midpoint E (a, b).