Class 10th Maths Chapter 1 Test Paper

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 $a$.

Find the equation of the line passing through the points P(1, 2) and Q(3, 4).

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.

Find the distance between the points A(-1, 2) and B(3, 4).

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.

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.

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.