windowtore.blogg.se - Analytical geometry formulas grade 11

Given the points A (–2 –1), B (5 6) and C (7 –2), calculate the size of ABC.

Determine the inclination of the straight line that passes through the points.

Line AB is perpendicular to CD, which has a gradient of –4.

Give your answers correct to two decimal places. Θ = 26,57 (rounded off to two decimal places) If tan θ = ½ , then θ = 26,56505 …° (Press: shift tan ½ on your calculator) To find the inclination of a line, or the angle it makes with the x-axis, we use tan θ.īA is also change in y which is the gradient of AB.Īngle θ shows the slope or inclination of the line AB. In trigonometry, you used the ratios tan θ, sin θ and cosθ. ∴ equation of line AB is y = ½ x + 2½ (2)

Line AB is perpendicular to CD, which has a gradient of –2.

Determine the equation of the straight line that passes through the points P(1 2) and Q(3 8) in the form y = .

Gradient and then substitute into y = mx + c. Two points on the line: first calculate the The gradient and the coordinates of at least Y = –2x +7 We usually put the answer in the form y = mx + c. Y – (–1) = –2(x – 4) substitute (4 –1) into the equation If the gradient of a line is –2 and the point (4 –1) lies on the line, find the equation of the line.y − y1 = m (x − x1) If the gradient of a line is –2 and the line cuts the y-axis at 1, then the equation of the line is y = –2x + 1. NOTE: y 1 and x 1 are the coordinates of a specific point on the line. You can also find the equation of a straight line using y − y 1 = m (x − x 1), if you know the gradient m and any point (x 1 y 1) on the line, or if two points given. You can find the equation of a straight line using y = mx + c, if you know the gradient m and the y-intercept c.

Diagonals of parallelogram ABCD bisect each other.

Use the information that you have to find the coordinates of point D.

Draw the parallelogram on squared paper.

(–4 7), B (4 5), C (0 –1) and D (a b) are the vertices of parallelogram ABCD. We can use coordinate geometry to identify the properties of geometricĪ.

Midpoint of KL = ( x 1 + x 2 y 1 + y 2).

If M (–1 4) is the midpoint of line segment AB, and the coordinates of A (3 6) are given, find the coordinates of the endpoint B. Determine the coordinates of the midpoint.

K (–1 –6) and L (5 4) are two coordinates on the same straight line. X as the midpoint of AB = x A + x B and y as midpoint of AB = y A + y B Find the coordinates of A if the coordinates of B are (4 -3). The coordinates of the midpoint of the line AB are (1 -4). So the midpoint has the coordinates (4½ 4) Where (x 1 y 1) and (x 2 y 2) are the endpoints of the line.įor a line passing through the two points A(6 6) and B(3 2), find the The midpoint of a line has the coordinates If you know the coordinates of the two endpoints of a line, you can find the point that is halfway between them. T = 0 or t = −6 (both solutions are correct – plot the points to see why!)(3)

Length AB = √(x 2 − x 1) 2 + (y 2 − y 1) 2Ġ = t (t + 6) (factorise by taking out the HCF).If PQ = 5 units P (5 t) and Q (1 –3) determine the possible value(s) of t.For a line passing through the two points A(6 6) and B(3 2), calculate the length of AB.The co-ordinates of P (5 2) and Q(3 t) are given. The length of the straight line PQ is given as 2 √5.L(-5 -2) and M (-1 -6) are two sets of co-ordinates on the same straight line.You can also find the coordinates for a point on the line using the distance formula. The graphs of y = 2x + 1 and y = − ½ x + 5 are perpendicular The graphs of y = 2x + 1 and y = 2x + 5 are parallel because they both have m = 2.Note: The equation must always be in form y = mx + c This means that the gradient of one line is the negative reciprocal of the gradient of the second line: The product of the gradients of lines that are perpendicular is –1. Where (x 1 y 1) and (x 2 y 2) are two points on the line. The steeper the gradient, the bigger the angle it makes with the ground or the positive side of the x-axis.

The gradient is the slope of a straight line. This topic is also called Coordinate Geometry Analytical geometry works with the Cartesian plane and with algebra to define points, lines and shapes. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the