please help! i don't get these problems at all!
a(4,3) b(7,4) and c(5,2) are midpoints of a triangle. find the coordinates for the vertices of the triangle!
Let the vertices be A, B, and C, where A is the vertex opposite a(4,3) etc.
let's work on the x's first,
let the corresponding x's be p, q, and r
(p+q)/2 = 7
p + q = 14 -- #1
in the same way...
p + r = 10 -- #2
q + r = 8 -- #3
subtract #1 - #2
q - r = 4
add that to #3
2q = 12
q = 6
then r = 2
and p = 8
now do the y's the same way.
wait what? I'm a bit confused here. so (4,3) would be on CB?
whats does corresponding x mean? and how did x appear?
Yes, (4,3) is on CB
(5,2) on AB and (7,4) on AC
I let the points be A(p, ?), B(q, ?) and C(r, ?)
I then followed the definition of finding midpoints.
Don't you add up the x values , then divide by 2 , to get the x of the midpoint?
Pick your own values for the y's, and follow the same method.
Sorry, but I got lost here...
I let the points be A(p, ?), B(q, ?) and C(r, ?)
^what does this?
I then followed the definition of finding midpoints.
Don't you add up the x values , then divide by 2 , to get the x of the midpoint?
To find the coordinates of the vertices of the triangle given the midpoints, we can use the Midpoint Formula and the properties of midpoints.
The Midpoint Formula states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by the coordinates:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
In this case, we have the midpoints of the triangle segments: a(4,3), b(7,4), and c(5,2).
To find the coordinates of the vertices of the triangle, we can double the x and y values of each midpoint. Here's how you can do it step by step:
1. Multiply the x-coordinate of each midpoint by 2.
Vertex A: 2 * 4 = 8
Vertex B: 2 * 7 = 14
Vertex C: 2 * 5 = 10
2. Multiply the y-coordinate of each midpoint by 2.
Vertex A: 2 * 3 = 6
Vertex B: 2 * 4 = 8
Vertex C: 2 * 2 = 4
So, the coordinates of the vertices of the triangle are:
Vertex A: (8, 6)
Vertex B: (14, 8)
Vertex C: (10, 4)
This means that the triangle with midpoints a(4,3), b(7,4), and c(5,2) has vertices at (8, 6), (14, 8), and (10, 4).