To determine the type of quadrilateral, we need to calculate the distances between the points.

The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2-x1)² + (y2-y1)²].

1. Distance QR = √[(-2-1)² + (-1-2)²] = √[9 + 9] = √18
2. Distance RS = √[(1+2)² + (-4+1)²] = √[9 + 9] = √18
3. Distance ST = √[(4-1)² + (-1+4)²] = √[9 + 9] = √18
4. Distance TQ = √[(1-4)² + (2+1)²] = √[9 + 9] = √18

Since all sides are equal, QRST is a rhombus.

Next, we need to check if it's a square or a rectangle. For this, we calculate the distances of the diagonals.

1. Distance QS = √[(1-1)² + (-4-2)²] = √[0 + 36] = 6
2. Distance RT = √[(-2-4)² + (-1+1)²] = √[36 + 0] = 6

Since the diagonals are equal, QRST is a square.

So, the correct answers are c. rhombus and d. square.

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To determine the type of quadrilateral, we need to calculate the distances between the points.

The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2-x1)² + (y2-y1)²].

1. Distance QR = √[(-2-1)² + (-1-2)²] = √[9 + 9] = √18
2. Distance RS = √[(1+2)² + (-4+1)²] = √[9 + 9] = √18
3. Distance ST = √[(4-1)² + (-1+4)²] = √[9 + 9] = √18
4. Distance TQ = √[(1-4)² + (2+1)²] = √[9 + 9] = √18

Since all sides are equal, QRST is a rhombus.

Next, we need to check if it's a square or a rectangle. For this, we calculate the distances of the diagonals.

1. Distance QS = √[(1-1)² + (-4-2)²] = √[0 + 36] = 6
2. Distance RT = √[(-2-4)² + (-1+1)²] = √[36 + 0] = 6

Since the diagonals are equal, QRST is a square.

So, the correct answers are c. rhombus and d. square.

Knowee AI · Accepted Answer

To determine the type of quadrilateral, we need to calculate the distances between the points.

The distance between two points (x1, y1) and (x2, y2) is given by the formula √[(x2-x1)² + (y2-y1)²].

1. Distance QR = √[(-2-1)² + (-1-2)²] = √[9 + 9] = √18
2. Distance RS = √[(1+2)² + (-4+1)²] = √[9 + 9] = √18
3. Distance ST = √[(4-1)² + (-1+4)²] = √[9 + 9] = √18
4. Distance TQ = √[(1-4)² + (2+1)²] = √[9 + 9] = √18

Since all sides are equal, QRST is a rhombus.

Next, we need to check if it's a square or a rectangle. For this, we calculate the distances of the diagonals.

1. Distance QS = √[(1-1)² + (-4-2)²] = √[0 + 36] = 6
2. Distance RT = √[(-2-4)² + (-1+1)²] = √[36 + 0] = 6

Since the diagonals are equal, QRST is a square.

So, the correct answers are c. rhombus and d. square.

Given the set of points as vertices of quadrilateral QRST, determine whether it is a rhombus, a rectangle, or a square. Choose all that apply.Q(1, 2), R(–2, –1), S(1, –4), T(4, –1)Question 8Select one or more:a.None of these b.Rectanglec.rhombusd.squaree.Kite

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