JEE MATHEMATICS MCQ: STRAIGHT LINES

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Consider the following statements.

I. Let

A\left(x_1, y_1\right), B\left(x_2, y_2\right)

and

{C}\left(x_3, y_3\right)

be the vertices of a triangle then centroid is

\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right)

II. If the point

P(x, y)

divides the line joining the points

A\left(x_1, y_1\right)

and

B\left(x_2, y_2\right)

in the ratio

m: n

(internally), then

x=\frac{m x_2+n x_1}{m+n}, y=\frac{m y_2+n y_1}{m+n}

Choose the correct option.

View answer and explanation

Correct option: C

Both are true

Option C (Both are true) is correct because both the centroid formula and the section formula (internal division) are stated accurately.

More Questions from STRAIGHT LINES

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x-3 y=p, a x+2 y=q

a x+y=r

\left\{ {a{t_1}{t_2},\;a\left( {{t_1} + {t_2})\} ,\{ a{t_2}{t_3},a({t_2} + {t_3}} \right)} \right\},\;\left\{ {a{t_3}{t_1},\;a\left( {{t_3} + {t_1}} \right)} \right\}

y = 2\;x + 4

6x = 3y + 5

{x^2} + {y^2} + 2xy - 8ax - 8ay - 9{a^2} = 0

(3,8)

x+3 y=7

\left( {{x^2} + 7xy + 2{y^2}} \right)\left( {y - 1} \right) = 0