The endpoint of MP are M(2,1) and P(14,10). If point K partitions MP in aratio of MK:KP=3:2, what are the coordinates of K?
Answers
Answer: The required co-ordinates of he point K are (9.2, 7).
Step-by-step explanation: Given that the the endpoint of MP are M(2,1) and P(14,10) and the point K partitions MP in the ratio of MK : KP = 3 : 2.
We are to find the co-ordinates of point K.
We know that
the co-ordinates of a point that divides the line joining the points (a, b) and (c, d) in the ratio m : n are given by
For the given division, m : n = 3 : 2.
Therefore, the co-ordinates of the point K are
Thus, the required co-ordinates of the point K are (9.2, 7).
2(2,1)(14,10)
(4,2) - (14,10)= (-10, -8)
The coordinates of K are (-10, -8).
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The m is the slope (rise over run or rate of change) and the b is the y-intercept (where this line crosses the y-axis).
So Think of rewriting this equation as:
y=-1.5x+9
Looks like y=mx+b doesn't it.
This means -1.5=m and thus the slope is -1.5.
b. the y axis
c. a horizontal line that passes through the point (1,4)
d. the x axis
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Step-by-step explanation:
(csc θ − 1) / cot θ
Multiply top and bottom by the conjugate csc θ + 1.
(csc θ − 1) (csc θ + 1) / (cot θ (csc θ + 1))
Distribute.
(csc²θ − 1) / (cot θ (csc θ + 1))
Use Pythagorean identity.
cot²θ / (cot θ (csc θ + 1))
Divide.
cot θ / (csc θ + 1)
g(x)=f(x)+n A horizontal shift of f , n units left
g(x)=f(x)- n A vertical shift of f, n units up
g(x)=f(x+n) A vertical shift of f, n units down
g(x)=f(x-n) A horizontal shift of f , n units right
Answers
Step-by-step explanation:
Transformations of graphs are fairly simple. Start with a parent function, or g(x) = f(x).
To move the graph UP or DOWN, add that number on the outside of the parenthesis with x: g(x) = f(x) + n is up, g(x) = f(x) - n is down.
To move the graph RIGHT you must SUBTRACT from inside the parenthesis. g(x) = f(x - n)
To move the graph to the LEFT you must ADD from inside the parenthesis . g(x) = f(x + n)