If the centroid of the triangle formed by (7, x), (y, -6) and (9, 10) is at (6, 3), then the values of x and y are:
Answer: A
The centroid averages the three vertices.
\[ \frac{7 + y + 9}{3} = 6 \quad\Longrightarrow\quad 16 + y = 18 \quad\Longrightarrow\quad y = 2 \]
\[ \frac{x - 6 + 10}{3} = 3 \quad\Longrightarrow\quad x + 4 = 9 \quad\Longrightarrow\quad x = 5 \]
Please log in or register to report this question.
The points (2, -2), (-2, 1), and (5, 2) are the vertices of a:
Answer: A
Let's find the slopes of the lines connecting the points.
Slope between (2,-2) and (-2,1) = \(\frac{1-(-2)}{-2-2} = \frac{3}{-4}\).
Slope between (-2,1) and (5,2) = \(\frac{2-1}{5-(-2)} = \frac{1}{7}\).
Slope between (5,2) and (2,-2) = \(\frac{-2-2}{2-5} = \frac{-4}{-3} = \frac{4}{3}\).
The product of the slopes of the first and third lines is \((-\frac{3}{4}) \times (\frac{4}{3}) = -1\). Since the product is -1, these two lines are perpendicular, forming a right angle. Therefore, the triangle is a right-angled triangle.
Please log in or register to report this question.
The equation of the line whose slope is -4/3 and which passes through (-3, 6) is:
Answer: A
Use the point-slope form.
\[ y - 6 = -\frac{4}{3}(x + 3) \]
\[ 3y - 18 = -4x - 12 \quad\Longrightarrow\quad 4x + 3y = 6 \]
Checking: at \( (-3, 6) \), \( -12 + 18 = 6 \).
Please log in or register to report this question.
