Straight Lines
Grade None
Question:
<p>The coordinates of a point dividing the line segment joining (1, 2) and (4, 5) externally in the ratio 2:1 is ________.</p>
<p style="display:inline">(6, 8)</p>
<p style="display:inline">(7, 8)</p>
<p style="display:inline">(8, 6)</p>
<p style="display:inline">(4, 5)</p>
Step-by-Step Solution
Key Concept: The external section formula calculates point coordinates by subtracting the weighted endpoint values and dividing by the difference of the ratio terms.
<p>(7, 8)<br />
The coordinates of a point dividing the line segment joining <span class="math-tex">$\left(x_1, y_1\right)$</span> and <span class="math-tex">$\left({x}_2, {y}_2\right)$</span> externally in the ratio m : n is <span class="math-tex">$\left(\frac{m x_2-n x_1}{m-n}, \frac{m y_2-n y_1}{m-n}\right)$</span>.<br />
So, the coordinates of a point dividing the line segment joining <span class="math-tex">$(1,2)$</span> and <span class="math-tex">$(4,5)$</span> externally in the ratio <span class="math-tex">$2: 1$</span> is <span class="math-tex">$\left(\frac{2 * 4-1 * 1}{2-1}, \frac{2 * 5-1 * 2}{2-1}\right)=(7,8)$</span>.</p>
Correct Answer: B