The points which trisect the line segment joining the points (0, 0) and (9, 12) are

Question

The points which trisect the line segment joining the points (0, 0) and (9, 12) are (A) (3, 4), (6, 8) (B) (8, 6), (0, 2) (C) (1, 3) (2, 5) (D) (4, 0), (0, 3)

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<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/ee54468f825f700c0a9593385d9cb6c4-.png" /> Let required point are P Q P ((9+2 × 0/1+2), (1 × 12+2 × 0/1+2)) divides in 1: 2 P=(3,4) Q divides in 2: 1 Hence Q ((2 × 9+1 × 0/2+1), (2 × 12+1+0/2+1))= Q (6,8)

Q. The points which trisect the line segment joining the points (0, 0) and (9, 12) are

(3, 4), (6, 8)

(8, 6), (0, 2)

(1, 3) (2, 5)

(4, 0), (0, 3)

Let required point are $P$ & $Q$
$P (\frac{9 + 2 \times 0}{1 + 2}, \frac{1 \times 12 + 2 \times 0}{1 + 2})$ divides in $1 : 2$
$P = (3, 4)$
Q divides in $2 : 1$
Hence $Q (\frac{2 \times 9 + 1 \times 0}{2 + 1}, \frac{2 \times 12 + 1 + 0}{2 + 1}) = Q (6, 8)$

Q. The points which trisect the line segment joining the points (0, 0) and (9, 12) are

(3, 4), (6, 8)

(8, 6), (0, 2)

(1, 3) (2, 5)

(4, 0), (0, 3)

Let required point are P & Q P(1+29+2×0​,1+21×12+2×0​) divides in 1:2 P=(3,4) Q divides in 2:1 Hence Q(2+12×9+1×0​,2+12×12+1+0​)=Q(6,8)

Let required point are $P$ & $Q$
$P (\frac{9 + 2 \times 0}{1 + 2}, \frac{1 \times 12 + 2 \times 0}{1 + 2})$ divides in $1 : 2$
$P = (3, 4)$
Q divides in $2 : 1$
Hence $Q (\frac{2 \times 9 + 1 \times 0}{2 + 1}, \frac{2 \times 12 + 1 + 0}{2 + 1}) = Q (6, 8)$