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zysi [14]
2 years ago
14

Find the point L such that JL and KL form a 3:1 ratio.

Mathematics
2 answers:
melomori [17]2 years ago
7 0
I graphed the points. 

It forms an imaginary right triangle where JK serves as the hypotenuse. We simply use the Pythagorean theorem to solve for the measure of the segment.

long leg: -3 to 4 = 7 units
short leg: -2 to 4 = 6 units

c² = a² + b²
c² = 7² + 6²
c² = 49 + 36
c² = 85
c = √85
c = 9.22 or 9

9/4 = 2.25
2.25 * 3 = 6.75

Among the given choices, (2.25,-0.5) is the closest point of L to the segment JK

lubasha [3.4K]2 years ago
6 0

Answer:

The correct option is 3.

Step-by-step explanation:

The coordinates of end points of a line segment are (-3,4) and (4,-2).

Using section formula.

(x,y)=(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})

It is given that point L such that JL and KL form a 3:1 ratio.

(x,y)=(\frac{3(4)+1(-3)}{3+1}, \frac{3(-2)+1(4)}{3+1})

(x,y)=(\frac{9}{4}, \frac{-2}{4})

(x,y)=(2.25, -0.5)

Therefore the correct option is 3.

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points a,b and c are collinear on AC, and AB:BC=3/4. A is located at (x,y), B is located at (4,1), and c is located at (12,5). w
olga_2 [115]
We have two unknowns: x and y. Now, we have to formulate 2 equations. The first would come from the use of the given ratio:

We use the distance formula to find the distance between coordinates:

3/4 = √[(x-4)²+(y-1)²] / √[(4-12)²+(1-5)²]
√[(x-4)²+(y-1)²]  = 3√5
(x-4)²+(y-1)² = 45
x² - 8x + 16 + y² - 2y + 1 = 45
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The second equation must come from the equation of a line:
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Substitute y=5 and x=12 for point (12,5)
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So, the second equation is

y = 1/2x -1 or x = 2 + 2y --> eqn 2

Solving the equations simultaneously:
(2 + 2y)² - 8(2 + 2y) + y² - 2y = 28 
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y = -2
x = 2+2(-2) = -2

Therefore, the coordinates of point A is (-2,-2).

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