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What is the value of y so that the line segment with endpoints A(−3, y) and B(6, −4) is parallel to the line segment with endpoints C(7, 6) and D(−2, 8)?

y = −7
 y = 1
 y=1/2
 y = −2

User Mithaldu
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2 Answers

4 votes

Final answer:

To make line segment AB parallel to line segment CD, we calculate the slope of CD and ensure AB has the same slope. The slope of CD is −1/4.5, and setting the slope of AB equal to this value leads to the conclusion that y = −2 for point A.

Step-by-step explanation:

To determine the value of y such that the line segment with endpoints A(−3, y) and B(6, −4) is parallel to the line segment with endpoints C(7, 6) and D(−2, 8), we need to ensure that the slope of line AB is equal to the slope of line CD. The slope m of a line passing through two points (x1, y1) and (x2, y2) is given by m = (y2y1) / (x2x1).

For line CD, the slope is (8 − 6) / (−2 − 7) = 2 / (−9) = −1/4.5. To find the value of y for point A so that line AB is parallel to CD, we need to set the slope of AB equal to −1/4.5:

(−4 − y) / (6 − (−3)) = −1/4.5
(−4 − y) / 9 = −1/4.5
−4 − y = −9 / 4.5
y = −4 + 2 = −2

Therefore, the correct value of y that makes line AB parallel to line CD is −2.

User Bayman
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7.9k points
5 votes
if both segments are parallel to each other, that means both segments have the same slope value, thus


\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ -3}}\quad ,&{{ y}})\quad % (c,d) B&({{ 6}}\quad ,&{{ -4}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-4-y}{6-(-3)}\implies \cfrac{-4-y}{6+3} \\\\\\ \boxed{\cfrac{-4-y}{9}}


\bf -------------------------------\\\\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) C&({{ 7}}\quad ,&{{ 6}})\quad % (c,d) D&({{ -2}}\quad ,&{{ 8}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{8-6}{-2-7}\implies \boxed{\cfrac{2}{-9}}\\\\ -------------------------------\\\\ \cfrac{-4-y}{9}=\cfrac{2}{-9}\implies -4-y=\cfrac{2\cdot 9}{-9}\implies -4-y=\cfrac{2}{-1} \\\\\\ -4-y=-2\implies -4+2=y\implies -2=y
User BlueZed
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