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4 Calculate the coordinates of B, where k < 0.

April 12, 2026Mathematics

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Answer

(-4; -4)

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here's the solution for 1.4:

1.4 Calculate the coordinates of $B$ , where $k < 0$ .

Use the gradient of $AB$ , $m_{AB} = 7$ , from 1.3 and the coordinates of $A(-2; 10)$ and $B(k; k)$ .
Apply the gradient formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .
$7 = \frac{k - 10}{k - (-2)}$ $7 = \frac{k - 10}{k + 2}$
Solve for $k$ .
$7(k + 2) = k - 10$ $7k + 14 = k - 10$ $7k - k = -10 - 14$ $6k = -24$ $k = \frac{-24}{6}$ $k = -4$
Since $B(k; k)$ and $k = -4$ , the coordinates of $B$ are $(-4; -4)$ .
This satisfies the condition $k < 0$ .
The coordinates of $B$ are $\boxed{(-4; -4)}$ .

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