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Question: A square PQRS has vertices P(2, 4) , Q(6, 8) , R(10, 4) and S(6, 0) . Which set of steps should a student follow to prove that the diagonals of the square are perpendicular to each other? Step 1 : Find the slope of diagonal PR (m1) and slope of diagonal QS (m2) . Step 2 : Show that m1=−m2 . Step 1 : Find the slope of diagonal PR (m1) and slope of diagonal QS (m2) . Step 2 : Show that m1+m2=−1 . Step 1 : Find the slope of diagonal PR (m1) and slope of diagonal QS (m2) . Step 2 : Show that m1=m2 . Step 1 : Find the slope of diagonal PR (m1) and slope of diagonal QS (m2) . Step 2 : Show that m1×m2=−1 .
To prove that the diagonals of a square are perpendicular, you need to show that the product of their slopes is \(-1\). The correct set of steps is: **Step 1:** Find the slope of diagonal \( PR \) (\( m_1 \)) and the slope of diagonal \( QS \) (\( m_2 \)). **Step 2:** Show that \( m_1 \times m_2 = -1 \). This indicates that the diagonals are perpendicular to each other. So, the correct choice is the last option: Step 1: Find the slope of diagonal PR (m1) and slope of diagonal QS (m2). Step 2: Show that m1×m2=−1.
The correct set of steps a student should follow is: Step 1: Find the slope of diagonal PR (m1) and slope of diagonal QS (m2). Step 2: Show that m1×m2=−1. This is because in geometry, two lines are perpendicular if the product of their slopes is -1. If m1 and m2 are the slopes of the two lines, then m1 * m2 should equal -1 for the lines to be perpendicular. Hence, this is the correct set of steps to prove that the diagonals of the square are perpendicular to each other.
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