Question

the distance between two points m and n on a graph is given as roots of 10 square n 7 square the point of m are -4,3 and n points lies in first quadrant, which of the following is true about the all possible x coordinates of point N?​

Answer 1

Answer:

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Let the given points be:

P(3, -6) = (x1, y1)

Q(-3, a) = (x2, y2)

Using distance formula,

Distance between the points P(3, -6) and Q(-3, a) is:

[(-3 – 3)2 + (a + 6)2] = 10 units (given)

Squaring on both sides of the equation,

(-6)2 + (a + 6)2 = 100

(a + 6)2 = 100 – 36 = 64

Taking root on both the sides, we get;

a + 6 = ±8

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Answer 2

Answer:

The x coordinate of point n will be a multiple of 3.

Step-by-step explanation:

Given:

Distance between m and n = $\sqrt{10^2 + 7^2}$

point m = ( -4, 3 )

We know,

The distance between two points is given by Distance Formula, that is

Distance =  $\sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}$

where (x₁, y₁) are coordinates of 1st point

and (x₂, y₂) are coordinates of 2nd point

Method:

We apply the distance formula for the given conditions.

Let the coordinates of point n be (x, y)

=>   $\sqrt{(x+4)^2 + (y-3)^2}$ =  $\sqrt{10^2 + 7^2}$

Squaring both sides,

=> (x + 4)² + (y - 3)² = 10² + 7²

On comparing,

either (x+4)² = 10² and (y-3)² = 7²  OR   (x+4)² = 7² and (y-3)² = 10²

Taking square root both sides in all,

=> x+4 = 10 and y-3 = 7         or      x+4 = 7 and y-3 = 10

=> x = 10 - 4 and y = 7 + 3     or     x = 7 - 4 and y = 10 + 3

=> x = 6 and y = 10                or          x = 3 and y = 13

Therefore, two possible coordinates of n are (6,10) and (3, 13)

Thus the x coordinate of point n will be a multiple of 3.