Question

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Answer 1

Distance between two points $(-3, 4)$ and $(5, -2)$ is $10$ units.

Mid-point of the line segment joining $(-1, -5)$ and $(7, 1)$ is  $(3, -2)$.

Degree of the given polynomial is $7$.

6) Distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

So, distance between two points $(-3, 4)$ and $(5, -2)$ is:

$=\sqrt{(5-(-3))^2+(-2-4)^2}$

$=\sqrt{(8)^2+(-6)^2}$

$=\sqrt{64+36}$

$=\sqrt{100}$

$=10$

So, option D is correct.

7) Mid-point of the line segment joining $(x_1, y_1)$ and $(x_2, y_2)$ is:

$(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Mid-point of the line segment joining $(-1, -5)$ and $(7, 1)$ is:

$(\frac{-1+7}{2}, \frac{-5+1}{2})$

$= (\frac{6}{2}, \frac{-4}{2})$

$= (3, -2)$

So, option A is correct.

8) Degree of a polynomial is the highest power of the variable in the polynomial.

$f(x)=3x^2-7x^4+9x^7+2x^3$

Here, the highest power of the variable is $7$.

So, option B is correct.

Learn more about distance formula, mid point formula, and degree of polynomial.

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