# What are the coordinates of the point 3/4 of the way from A to B?

What are the coordinates of the point 3/4 of the way from A to B?

$What are the coordinates of the point 3/4 of the way from A to B?$

## This Post Has 6 Comments

1. nyny2129 says:

(-3.5, 1.25)

Step-by-step explanation:

Given:

A(-5, -4)

B(-3, 3)

Required:

Coordinates of the point 3/4 of the distance between A and B.

SOLUTION:

Find the coordinates using the formula below:

$(x, y) = (x_1 + k(x_2 - x_1), y_1 + k(y_2 - y_1))$

Let,

$A(-5, -4) = (x_1, y_1)$

$B(-3, 3) = (x_2, y_2)$

$k = \frac{3}{4}$

Plug in the values into the formula:

$(x, y) = (-5 + \frac{3}{4}(-3 -(-5)), -4 + \frac{3}{4}(3 -(-4))$

$(x, y) = (-5 + \frac{3}{4}(2), -4 + \frac{3}{4}(7)$

$(x, y) = (-5 + \frac{3*2}{4}, -4 + \frac{3*7}{4}$

$(x, y) = (-5 + 1.5, -4 + 5.25)$

$(x, y) = (-3.5, 1.25)$

The coordinates of the point 3/4 from A to B are (-3.5, 1.25).

2. insaneshootermo says:

The coordinates of the point at 3/4 of the distance from A to B from A is (-3.5, 1.25)

Step-by-step explanation:

The coordinates of the point A is (-5, -4),

The coordinates of the point B is (-3, 3)

Let the point 3/4 from A to B = P

The coordinates of the point 3/4 from A to B is found as follows;

(-5 + (3/4×(-3 - (-5)), -4 + 3/4×(3 - (-4)) which gives;

The coordinates of the point 3/4 from A to B as P(-3.5, 1.25)

We verify the length from A to B  and from A to P as follows;

The distance l between two points (x₁, y₁) and  (x₂, y₂) is given by the formula;

$\sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

For AB, we have;

$Length \ of \ segment \ \overline {AB} = \sqrt{\left (3-(-4) \right )^{2}+\left ((-3)-(-5) \right )^{2}}=\sqrt{53} \approx 7.28$

$Length \ of \ segment \ \overline {AP} = \sqrt{\left (1.25-(-4) \right )^{2}+\left ((-3.5)-(-5) \right )^{2}}= \dfrac{3}{4} \cdot \sqrt{53}$

Therefore, the point P (-3.5, 1.25) is the point 3/4 distance of A to B from A.

3. ordonez9029 says:

Dm me for the answer can’t do it rn

4. gracepiechowiak says:

$P(x,y) = (7,6)$

Step-by-step explanation:

Given

$X = (1,-6)$

$Y = (9,10)$

$Point = \frac{3}{4}$

Required

Determine the coordinate of the point;

First, we need to determine the ratio of the point between X and Y

Represent the point with P

If the distance between point X and point P is $\frac{3}{4}$,

The distance between point P and point Y will be $1 - \frac{3}{4} = \frac{1}{4}$

$Ratio = XP : PY$

$Ratio = \frac{3}{4} : \frac{1}{4}$

Multiply through by 4

$Ratio = 3: 1$

Now, the coordinate of P can be calculated using

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

Where

$m:n = 3:1$

$(x_1,y_1) = (1,-6)$

$(x_2,y_2) = (9,10)$

Substitute these values in the formula above

$P(x,y) = (\frac{3 * 9 + 1 * 1}{3+1},\frac{3 * 10 + 1 * -6}{3+1})$

$P(x,y) = (\frac{27 + 1}{4},\frac{30 -6}{4})$

$P(x,y) = (\frac{28}{4},\frac{24}{4})$

$P(x,y) = (7,6)$

5. aebacchieri says:

(3.5,5.25)

Step-by-step explanation:

the difference between the x values are 2 and dividing that by 4 is 0.5 and multiply by 3 as it is three quarters of the way so it equals 1.5. Move point a on its x axis to the value 3.5. the difference between the y values is 7 and dividing that by 4 is 1.75 and multiply by 3 which is 5.25. move points on its y axis to the value 1.25. the end coordinates are (3.5,5.25)

6. Spence8900 says:

Coordinates of the point P are $(-\frac{29}{7},-1)$

Step-by-step explanation:

If a point P(x, y) divides the line AB into the ratio of m : n, coordinates of this point will be,

x = $\frac{mx_2+nx_1}{m+n}$

y = $\frac{my_2+ny_1}{m+n}$

In the given question m : n = 3 : 4

And the coordinates of A and B are (-5, -4) and (-3, 3) respectively.

x = $\frac{3(-3)+4(-5)}{3+4}$

x = -$\frac{29}{7}$

y = $\frac{3(3)+4(-4)}{3+4}$

y = -1

Therefore, coordinates of the given point P are $(\frac{29}{7},-1)$.