Q1. In coordinate geometry, what is the slope of the line passing through the points (2, 3) and (4, 7)?
Solution:
The slope of a line is calculated using the formula (y2 - y1) / (x2 - x1). For the points (2, 3) and (4, 7), the slope is (7 - 3) / (4 - 2) = 4 / 2 = 2.
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Q2. If a quadrilateral is a rectangle, which of the following statements is true?
Solution:
In a rectangle, opposite sides are equal in length.
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Q3. In a trapezoid, if the lengths of the two parallel sides are 8 cm and 5 cm, what is the length of the midsegment?
Solution:
The length of the midsegment of a trapezoid is the average of the lengths of the two parallel sides. Therefore, (8 cm + 5 cm) / 2 = 6.5 cm.
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Q4. What type of polygon is a shape with 5 sides?
Solution:
A polygon with 5 sides is called a pentagon.
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Q5. In a rectangle, if the length is doubled and the width remains the same, how does the area change?
Solution:
If the length is doubled, the new area becomes 2 × length × width, which is double the original area.
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Q6. In a trapezoid, if the lengths of the two parallel sides are 8 cm and 12 cm, what is the length of the midsegment?
Solution:
The length of the midsegment of a trapezoid is the average of the lengths of the two parallel sides. Therefore, midsegment = (8 cm + 12 cm) / 2 = 10 cm.
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Q7. If the diagonals of a rhombus are 6 cm and 8 cm, what is the area of the rhombus?
Solution:
The area of a rhombus can be calculated using the formula (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals. Thus, the area is (6 cm * 8 cm) / 2 = 24 cm².
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Q8. If a trapezoid has bases of lengths 10 cm and 6 cm, and a height of 4 cm, what is its area?
Solution:
The area of a trapezoid is calculated using the formula (1/2) × (base1 + base2) × height. Therefore, area = (1/2) × (10 cm + 6 cm) × 4 cm = 32 cm².
