Distance of the point P(3,-4) from the oirgin is?

Mathematics

2 answers:

krek1111 [17]3 years ago

5 0

Answer:

Distance between origin and point P(3, -4) is 5 units.

Solution:

We need to find distance between origin and point P (3, -4) .

We will be using distance formula. According to the distance formula , distance d between two points $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right) \text { and }\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)$ is given by

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

In given case two points are O ( 0 , 0 ) (origin) and P( 3 , -4) .

On applying distance formula

$\begin{aligned} \mathrm{OP} &=\sqrt{(3-0)^{2}+((-4)-0)^{2}} \\ &=\sqrt{3^{2}+(-4)^{2}} \\ &=\sqrt{9+16} \\ &=\sqrt{25} \end{aligned}$

So OP = 5 units

Hence distance between origin and point P(3, -4) is 5 units.

Naily [24]3 years ago

4 0

Answer:Answer: point (3,-4) is 3 units to the right of the origin and 4 down

Step-by-step explanation: easiest to graph

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Give a geometric description of the following system of equations.a. 2x−4y=12 −3x+6y=−15.b. 2x−4y=12 −5x+3y=10.a. 2x−4y=12 −3x+6

Reptile [31]

Answer:

a. No solution, parallel lines.

b. One solution.

Step-by-step explanation:

Given the system of equations:

a. $2x-4y=12$

$-3x+6y=-15$

b. $2x-4y=12$

$-5x+3y=10$

To give a geometric description of the given system of equations.

The geometric description of a system of equations in 2 variables mean the system of equations will represent the number of lines equal to the number of equations in the system given.

i.e.

Number of planes = Number of variables

Number of lines = Number of equations in the system.

Here, we are given 2 variables and 2 equation in each system.

So, they can be represented in the xy-coordinates plane.

And the number of solutions to the system depends on the following condition.

Let the system of equations be:

$A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0$