Mathematics, 23.06.2019 05:40 jennifercastill3

Find the coordinates of the point which divides the join of (-1,7) and (4,-3) in the ratio 2: 3

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Answer from: ndh64

To solve our given problem we will use section formula :]

Section Formula states that, when a point divides a line segment internally in the ratio m:n, So the coordinates are :]

$\tiny: \implies (x,y) = \bigg \lgroup x = \frac{m. {x}_{2} +n. {x}_{1} }{m + n} ,y= \frac{m. {y}_{2} +n. {y}_{1} }{m + n} \bigg \rgroup \\ \\ \\$

Let

(-1 , 7) = (x₁ , y₁)

(4 , -3) = (x₂ , y₂)

m = 2

n = 3

Upon Substituting coordinates of our given points in section Formula we get :]

$\tiny: \implies (x,y) = \bigg \lgroup x = \frac{2 \times 4 +3 \times - 1 }{2 + 3} ,y= \frac{2 \times - 3 +3 \times 7}{2 + 3} \bigg \rgroup \\ \\ \\$

$\tiny: \implies (x,y) = \bigg \lgroup x = \frac{8 - 3 }{2 + 3} ,y= \frac{ - 6 +21}{2 + 3} \bigg \rgroup \\ \\ \\$

$\tiny: \implies (x,y) = \bigg \lgroup x = \frac{5 }{5} ,y= \frac{15}{5} \bigg \rgroup \\ \\ \\$

$\tiny: \implies (x,y) = \bigg \lgroup x = 1,y= 3 \bigg \rgroup \\ \\$

Answer from: marieb39

The coordinates of the point in question is (1, 3).

Step-by-step explanation:

Point (-1, 7) is above and to the left of the point (4, -3). The point in question is to the right and below the point (-1, 7).

What will be the horizontal distance between the point (-1, 7) and the point in question?

The horizontal distance between the point (-1, 7) and (4, -3) is 5. Let the horizontal distance between the point (-1, 7) and the point in question be . Let the horizontal distance between the point in question and point (4, -3) be .

$\displaystyle \frac{a}{b} = \frac{2}{3}$ .

$\displaystyle a = \frac{2}{3} \; b$ .

$\displaystyle b = \frac{3}{2}\; a$ .

However,

a + b = 5 .

$\displaystyle a + \frac{3}{2}\; a = 5$ .

$\displaystyle \frac{5}{2}\; x= 5$ .

a = 2 .

In other words, the point in question is 2 units to the right of the point (-1, 7). The x-coordinate of this point shall be -1 + 2 = 1 .

The vertical distance between the point (-1, 7) and the point (4, -3) is 10. Similarly, the point in question is $(2/5) \times 10 = 4$ units below the point (-1, 7). The y-coordinate of this point will be 7 - 4 = 3 .

Thus, the point in question is (1, 3).

Answer from: Quest

if he has no friends he cant give them out to his friends

step-by-step explanation:

no friends = cant give anything out

Answer from: Quest

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is

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Find the coordinates of the point which divides the join of (-1,7) and (4,-3) in the ratio 2: 3...