Questions and Answers
If the points A(2, 3) and B(4, 5) lie on the graph of the linear equation $ax + by + c = 0$, then find the value of $a$.
$a = -2$
Find the equation of the line passing through the points P(1, 2) and Q(3, 4).
$y = x + 1$
If the coordinates of two points A and B are (2, 3) and (4, 5) respectively, then find the slope of the line segment AB.
$m = 1$
Find the distance between the points A(-1, 2) and B(3, 4).
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Find the coordinates of the point which divides the line segment joining the points A(2, 3) and B(4, 5) internally in the ratio 3:4.
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Study Notes
Linear Equations
- To find the value of 'a' in the linear equation ax + by + c = 0, we need to use the points that lie on the graph of the equation, such as A(2, 3) and B(4, 5).
- The equation of the line passing through two points P(1, 2) and Q(3, 4) can be found using the point-slope form or slope-intercept form.
Slope of a Line Segment
- The slope of the line segment AB can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) = (2, 3) and (x2, y2) = (4, 5) are the coordinates of points A and B respectively.
Distance Between Two Points
- The distance between two points A(-1, 2) and B(3, 4) can be found using the distance formula: √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) = (-1, 2) and (x2, y2) = (3, 4) are the coordinates of points A and B respectively.
Section Formula
- The coordinates of the point that divides the line segment joining the points A(2, 3) and B(4, 5) internally in the ratio 3:4 can be found using the section formula: ((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n)), where m:n is the ratio 3:4.
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Description
Test your understanding of linear equations and coordinates with this 20-mark quiz, complete with solution sheet in PDF format. Questions cover topics such as finding values, equations of lines, and distances between points.
