Pergunta

QUAD is a quadrilateral with vertices Q(-3,2),U(3,0),A(6,-5) and D(0,-3) The slope for overline (QU) is (0-2)/(3-(-3))=-(1)/(3) The slope for overline (UA) is (-5-1)/(6-3)=-(5)/(3) The slope for overline (AD) is (-3-(-5))/(0-6)=-(1)/(3) The slope for overline (DQ) is (-3-2)/(0-(-3))=-(5)/(3) So. __ Therefore,QUAD is a parallelogram What is the missing step in the proof? A. overline (QU)bot overrightarrow (AD) overline (UA)bot overline (DQ) because the segments have the same slope. B. overline (QU)Vert overline (AD) and overline (UA)Vert overline (DQ) because the product of the slopes is -1 C. overline (QU)Vert overline (AD) and overline (UA)Vert overline (DQ) because the segments have the same slope. D. overline (QU)bot overline (AD) and overline (UA)bot overline (DQ) because the product of the slopes is -1
Solução

4.1234 Voting

KaiqueProfissional · Tutor por 6 anos
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C. \( \overline{Q U} \parallel \overline{A D} \) and \( \overline{U A} \parallel \overline{D Q} \) because the segments have the same slope.
Explicação
## Step 1<br />The problem involves the properties of a parallelogram and the concept of slopes in coordinate geometry. The vertices of the quadrilateral QUAD are given as Q(-3,2), U(3,0), A(6,-5), and D(0,-3). The slopes of the sides of the quadrilateral are calculated and compared.<br /><br />## Step 2<br />The slopes of the sides QU, UA, AD, and DQ are calculated as -1/3, -5/3, -1/3, and -5/3 respectively. <br /><br />## Step 3<br />The slopes of the sides QU and AD are equal, and the slopes of the sides UA and DQ are also equal. This indicates that the sides of the quadrilateral are parallel.<br /><br />## Step 4<br />The missing step in the proof is the statement that the sides of the quadrilateral are parallel because the slopes of the sides are equal. This is the definition of parallel lines in coordinate geometry.
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