Ray BD bisects ∠ABC so that m∠ABD = 5y – 3 and m∠CBD = 2y +12. Find the value of y.
The midpoint of Line Segment AB is (2, -9). The coordinates of one endpoint are A (4, 10). Find the coordinates of endpoint B.
Find the distance between points F (7, 21) and G (-5, 18) to the nearest tenth.
not helpful need answer
5y-3-2y=12
3y-3=12
3y-3+3=12+3
3y=15
y=5
To find the value of y in the first question, we can use the fact that the angle bisector of ∠ABC divides it into two congruent angles. Therefore, we can set up an equation:
m∠ABD = m∠CBD
Substituting the given expressions:
5y – 3 = 2y + 12
Now, solve the equation:
5y - 2y = 12 + 3
3y = 15
y = 5
So, the value of y is 5.
For the second question, we are given the midpoint of Line Segment AB and one endpoint A. We can use the midpoint formula to find the coordinates of endpoint B. The midpoint formula states that the coordinates of the midpoint (M) of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are given by:
M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
We are given the midpoint as (2, -9) and one endpoint A as (4, 10). Using the midpoint formula, we can solve for the coordinates of endpoint B:
2 = (4 + x₂) / 2 --> 4 + x₂ = 4
-9 = (10 + y₂) / 2 --> 10 + y₂ = -18
From the first equation, we find that x₂ = 0. From the second equation, we find that y₂ = -28.
Therefore, the coordinates of endpoint B are (0, -28).
For the third question, we can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Given the points F (7, 21) and G (-5, 18), we can substitute the coordinates into the distance formula:
d = √((-5 - 7)² + (18 - 21)²) --> d = √((-12)² + (-3)²) --> d = √(144 + 9) --> d = √153
To find the distance to the nearest tenth, we can calculate the square root of 153:
d ≈ 12.37
Therefore, the distance between points F (7, 21) and G (-5, 18) is approximately 12.37 units.
"bisect" means to cut into equal parts.
Thus: 5y – 3 = 2y +12
etc
#2 , let the endpoint be (x,y)
for the x:
(4+x)/2 = 2
4+x = 4
x = 0
for the y:
---- your turn
#3, just use your "distance between 2 points" formula