Geometry

Miscellaneous

Medium

If the two vertices of a triangle are (5,4), and (-2,4) and the centroid is (5,6), then the third vertex is:

(10, 12)

(-10, 12)

(12, -10)

(12, 10)

✅ Correct Option: 4

The centroid of a triangle with vertices $(x_1, y_1)$ , $(x_2, y_2)$ , and $(x_3, y_3)$ is given by:

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

Given vertices: $(5, 4)$ , $(-2, 4)$ , and $(x, y)$

Given centroid: $(5, 6)$

For the $x$ -coordinate of the centroid:

$5 = \frac{5 + (-2) + x}{3}$

$5 = \frac{3 + x}{3}$

$15 = 3 + x$

$x = 12$

For the $y$ -coordinate of the centroid:

$6 = \frac{4 + 4 + y}{3}$

$6 = \frac{8 + y}{3}$

$18 = 8 + y$

$y = 10$

Therefore, the third vertex is $(12, 10)$ .

2025: 22 May Shift 2

The equation of the line which makes equal intercepts on the axis and passes through the point (2,5) shall be:

2025: 3 June Shift 2

What is the value of x for which the points A (-1, 3), B (2, x) and C (5, -1) are collinear?

2025: 20 May Shift 1

If area of a square is 44 cm², find the area of the circle formed by the same perimeter.

2025: 13 May Shift 2

(A). The angles of depression of two ships from the top of a lighthouse are $60^\circ$ and $45^\circ$ towards the east. If the ships are $300$ meter apart, the height of the lighthouse is $150(3+\sqrt{3})$

(B). If the surface area of a cube is $726 \text{ m}^2$ , then its volume shall be $1331 \text{ m}^3$

Determine as to which of the statements given above are correct :

2022: 6 Aug Shift 1

The perimeter of the figure is:

2025: 20 May Shift 2

Point A (4, 2) divides segment BC in the ratio 2:5. Coordinates of B and C are (2,6), (9,y) respectively. Find the value of y.

If the two vertices of a triangle are (5,4), and (-2,4) and the centroid is (5,6), then the third vertex is:

Solution

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